UNIT: WORKING WITH EXPONENTS
Based on the pattern in the table, what is the value of a?Powers of 2Valuea
1/64
What is the quotient? 9
1/9
Hector is rewriting the expression in expanded form. How many terms will be multiplied in his rewritten expression? 2 7 11 12
11
What is the base of the expression 11^12 3 11 12 21
11
What is the base of the expression ? 3 11 12 21
11
What is the value of n in the equation below? 3 6 12 27
12
What is the value of c in the equation below? 3 5 125 625
125
Which expression is equivalent to 14 X 14?
14^2
Which expression is equivalent to ?
14^2
Which pair of expressions has equivalent values? and and and and
1^13 and 1^15
Nadine and Calvin are simplifying the expression .Nadine claims the first step to simplify the expression is to raise the numerator and denominator to the power of 4 to get .Calvin claims the first step to simplify the expression is to apply the quotient of powers to get .Who is correct and why? Nadine is incorrect because she should have applied the quotient of powers rule first. Nadine is correct because she correctly applied the power of a product rule. Calvin is incorrect because he should have applied the power of a product rule first. Calvin is correct because he correctly applied the quotient of powers rule.
Calvin is correct because he correctly applied the quotient of powers rule.
A scientist looks at a bacterium and a virus in a lab. The bacterium has a diameter of meters. The virus has a diameter of meters. Which statement accurately compares the sizes of the specimens? The diameter of the bacterium is 10 times greater than that of the virus. The diameter of the bacterium is times as great as that of the virus. The diameter of the virus is 10 times greater than that of the bacterium. The diameter of the virus is times as great as that of the bacterium.
The diameter of the bacterium is 10 times greater than that of the virus.
Which equation finds the volume of a cube with a side length of 2n^6 units? cubic units cubic units cubic units cubic units
a
Which applies the power of a power rule to simplify the expression (8^12)^3
b
What is the pattern in the values as the exponents increase?Powers of 3Value139 add 3 to the previous value subtract 3 from the previous value divide the previous value by 3 multiply the previous value by 3
multiply the previous value by 3
Which expression shows the simplified form of ?
not (8r^-5)^-3
What is the value of ? 0 1
not - 1/196
What is the quotient? 7 343
not -7
Which is the value of this expression when and ? -8 8
not -8
What is the value of n in the equation below? 9 20
not -9
What is the value of k in the product of powers below? 0 1
not 0
Which expressions are equivalent to ? Check all that apply.
not 1 and 6
Which is the simplified form of the expression ?
not 1/4x^2y^16
Which expression has twice the value of ?
not 2^10
What is the value of n in the equation below? 3 6 12 27
not 3
What is the value of ?
not 3/1000
What is the value of y in the product of powers below?
not 6
Which is the simplified form of the expression ?
not 6^30
Which expressions have a value of ? Check all that apply.
not a c e
Which is the value of this expression when and ? -64 64
not b
Geoffrey is evaluating the expression as shown below.What are the values of a, b, c, and d?
not d
Which expression is equivalent to (q^6)^2
not d
Which is the simplified form of the expression ?
not q^30
Which conversions from scientific notation to standard notation are true? Select the four correct answers.
2,5,7,8
What is the value of in scientific notation?
2.226 x 10^8
The product of and a number n results in . What is the value of n?
2.6 x 10^12
What is the value of the expression, written in standard form?
200
Which expression is rewritten in exponential form?
m^5
What is the pattern in the values as the exponents increase?Powers of 2Value1 add to the previous value subtract from the previous value divide the previous value by 2 multiply the previous value by 2
multiply the previous value by 2
Which expression is equivalent to ? 12xy 7xy
y^3z^4
Which expression is equivalent to yxyxyxzxzxzxz 12xy 7xy
y^3z^4
Which expressions have a value of ? Check all that apply.
1 and 4
Which expressions can be simplified as ? Check all that apply.
1 and 5
Which expression is equivalent to ?
(6x6x6x6)x(6x6x6)
A cell phone weighs about pounds. Which value of n is most reasonable? 0 1
-1
What is the value of b in the equation below? 9 16
-10
What is the value of ? -15,625 -30 30 15,625
-15,625
What is the value of b in the equation ? -405 -5 5 405
-5
Which is the value of this expression when and ? -64 64
-64
What is the value of x in the product of powers below? 7 11
-7
Which is the value of this expression when and ? 360 720
-720
What is the value of y in the product of powers below?
0
Which answer shows written in standard form? -0.000009 -0.00009 0.0009 0.00009
0.00009
Which number is equal to ? -1,000 -30 0.001 0.003
0.001
What is the value of ? 0 1 undefined
1
Which is the simplified form of ? p 0 1
1
There are bytes in a gigabyte. There are bytes in a megabyte. How many times greater is the storage capacity of a 1-gigabyte flash drive than a 1-megabyte flash drive? 3 times greater 10 times greater 1,000 times greater 3,000 times greater
1,000 times greater
Which expressions have a value of ? Check all that apply.
1,2,4,6
The quotient of and a number n results in . What is the value of n?
1.5 x 10^-18
Which number is greatest?
1.997x10^2
The simplified form of an expression is . Which expression was simplified?
1/256 t^28
What is the value of c in the equation below?
1/4
What is the quotient?
1/5^9
Which is the simplified form of the expression ?
1/6^9
Which is the value of this expression when and ? -8 8
1/8
Which number is equal to ? 40 1,000 10,000 40,000
10,000
Terri is rewriting in expanded form. How many factors should she use in her expression?
13
Estimate the following product in scientific notation, and then select the best answer for the product's power of 10. 2.7 14 15 27
15
A 747 airplane weighs about 600,000 pounds. It can also be expressed as approximately tons. If there are 2,000 pounds in 1 ton, which is the most reasonable value of n? -2 -1 2 4
2
Jayne evaluated an expression that has a value of . Which expression could Jayne have evaluated? Check all that apply.
2 and 3
The product of and a number n results in . What is the value of n?
2 x 10^16
Which statements are true regarding the expression below? Check all that apply. The last factor, 8, with no exponent shown is equivalent to . The sum of the exponents is . The value of the expression is . The value of the expression is . An equivalent expression is . An equivalent expression is .
2,4,5
Which choices are correctly written in scientific notation? Select the four correct answers.
2,4,6,7
Which is the value of this expression when and ? 75
25/9
If c is a number with no exponent, what is the value of c in the equation below?
256
What is the value of the expression ?
256
Karim builds a wooden table. in.The rectangular top of his table has an area of square inches and a length of inches. What is the width of the table top? 9 inches 27 inches 2,187 inches 59,049 inches
27
Karim builds a wooden table. in.The rectangular top of his table has an area of square inches and a length of inches. What is the width of the table top? 9 inches 27 inches 2,187 inches 59,049 inches
27 inches
What is the value of ?
27/1000
Which expression is equivalent to 2(5)^4
2x5x5x5x5
Which expression is equivalent to ?
3(5)^6
Which expressions are equivalent to ? Check all that apply.
3,4,6
Which statement is correct?
3.56x10^2/1.09x10^4 > (aka c)
Which is the best estimate for written in scientific notation?
3x10^4
To best estimate the quotient in scientific notation, what number should replace m?
4
What is the value of b in the equation below? 3 4 5 8
4
Which number is written in scientific notation?
4.5x10^-3
Which number is greatest?
6.23x10^12
Which number is greatest?
6.23x10^2
What is in scientific notation?
6.82 x 10^12
What is the value of ?
625
Which is the best estimate for written in scientific notation?
6x10^-4
Which expression is equivalent to 6^3
6x6x6
Which expression is equivalent to ?
7*7*7*7*7/7*7
When evaluating , what will be the exponent of 10 in the product? 3 5 8 15
8
Which answer shows written in standard form? 0.000845 8,450 84,500 8,450,000
84,500
The area of a square is square units. What is the side length of one side of the square? units units units units
8n^18units
What is the value of n in the equation below? 9 20
9
Which expression is equivalent to ?
9*9*9*9*9
Which expression is equivalent to 9^5
9x9x9x9x9
The table below shows metric units of mass, with the relationship of each unit to 1 gram represented as a power of 10.Metric Units of MassUnitsPower of 10MicrogramMilligramCentigramGramKilogramWhich statement comparing these measures is true? A microgram is 1,000 times greater than a milligram. A milligram is 10 times greater than a centigram. A centigram is 100 times greater than a microgram. A kilogram is 100,000 times greater than a centigram.
A kilogram is 100,000 times greater than a centigram.
Which statement describes what these four powers have in common? All the powers have a value of 0 because the exponent is zero. All the powers have a value of 1 because the exponent is zero. All the powers have a value of -1 because the exponent is zero. All the powers have a fractional value because the exponent is zero.
All the powers have a value of 1 because the exponent is zero.
Tyler simplified the expression . His procedure is shown below.What is Tyler's error? Both powers should be in the numerator with positive exponents. Both powers should be in the denominator with positive exponents. The power should be in the numerator and the power in the denominator. The power should be in the numerator and the power in the denominator.
Both powers should be in the denominator with positive exponents.
Mr.Walden wrote the expression . He asked his students to write an equivalent expression of in simplified form.Four students wrote these expressions.IsaacRosaBruceBriannaWhich student is correct? Isaac Rosa Bruce Brianna
Brianna
Eli claims that the product of and is . Which explains whether Eli is correct? Eli is correct. He added to find the exponent of 2. Eli is incorrect. He added the exponents instead of subtracting them. Eli is incorrect. He subtracted the exponents instead of adding them. Eli is incorrect. He added the exponents even though the bases are not the same.
Eli is incorrect. He added the exponents even though the bases are not the same.
Stephen evaluated . His work is shown below. Which two statements describe the errors Stephen made? He changed the sign of the coefficient. A negative exponent does not affect the sign of a coefficient in scientific notation. The sign of the exponent determines the direction the decimal is moved in. He rewrote incorrectly; . The exponent is increased to account for the extra place the decimal is moved. He did not correctly evaluate the exponent. It should be evaluated as since exponents are evaluated using the same operation as the coefficients. He got the wrong value for the coefficients; is not possible. The coefficients in scientific notation are always greater than 1, but less than 10. He multiplied the coefficients; he should have added 6.34 and 4.5. The product of powers rule states that coefficients are added.
He changed the sign of the coefficient. A negative exponent does not affect the sign of a coefficient in scientific notation. The sign of the exponent determines the direction the decimal is moved in. He rewrote incorrectly; . The exponent is increased to account for the extra place the decimal is moved.
Jim's work evaluating is shown below.Which statement best describe Jim's first error? He did not multiply by 2 before applying the power. He did not apply the power to the denominator of . He did not evaluate 33 correctly. He did not multiply by 2 correctly.
He did not apply the power to the denominator of .
Pablo simplified the expression as shown. Which statement explains Pablo's error? He should have added the exponents instead of multiplying them. He should have divided the exponents instead of multiplying them. He should have found 8 as the exponent, not -8. He should have written as
He should have found 8 as the exponent, not -8.
Kailey wrote 8,912,000 in scientific notation as . Which statement best describes Kailey's work? Kailey is correct: equals 8,912,000. Kailey is not correct: the exponent of ten should be negative. Kailey is correct: it is written as a decimal number multiplied by a power of ten. Kailey is not correct: is not written in scientific notation.
Kailey is not correct: is not written in scientific notation.
Ramesh examined the pattern in the table.Powers of 7Value2,4013434971Ramesh says that based on the pattern . Which statement explains whether Ramesh is correct? Ramesh is correct because is equivalent to , which has the same value as . Ramesh is correct because as the exponents decrease, the previous value is divided by 7, so . Ramesh is not correct because is equivalent to , which has the same value as . Ramesh is not correct because as the exponents decrease, the previous value is divided by 7, so .
Ramesh is not correct because as the exponents decrease, the previous value is divided by 7, so .
Selena and Drake are evaluating the expression , when .Selena's WorkDrake's WorkWho is correct and why? Selena is incorrect because she should have substituted the values for the variables first, and then simplifed. Selena is correct because she simplified correctly and then evaluated correctly after substituting the values for the variables. Drake is incorrect because he should have simplified first, before substituting the values for the variables. Drake is correct because he substituted the values for the variables first, and simplified correctly.
Selena is correct because she simplified correctly and then evaluated correctly after substituting the values for the variables.
Fatima evaluated the expression , when and . Her work is shown below. What was Fatima's error? She subtracted the exponents incorrectly when simplifying the expression. She substituted the wrong values for the variables. She applied the exponent to instead of applying the exponent to just . She found an incorrect value for since the value should be negative.
She applied the exponent to instead of applying the exponent to just .
Ruchi measured the area of her kitchen as square units. When she recorded the area, she wrote square feet. Which statement about her labeling of the units is true? She is correct because dimensions of rooms must always be measured in feet and area would be square feet. She is correct because ft is equivalent to 2, 810 ft, which is an average size for a kitchen since area is always so much more than length. She is incorrect because is around 30,000 so the units must be smaller than feet. She most likely measured in inches. She is incorrect because 2.81 is a small number. She probably measured in yards to arrive at such a small value.
She is incorrect because is around 30,000 so the units must be smaller than feet. She most likely measured in inches.
Haley's work evaluating is shown below.Which statement best describe Haley's first error? She used the wrong number as a repeated factor and should have evaluated. She used the wrong number as a repeated factor and should have evaluated . She misinterpreted the exponential form and should have multiplied -2 and 8. She made a sign error when multiplying and should have had 256 as a final answer.
She made a sign error when multiplying and should have had 256 as a final answer.
Lauren simplified the expression as shown. Which statement explains Lauren's error? She should have subtracted the exponents instead of adding them. She should have multiplied the exponents instead of adding them. She should have found -2, not , as the exponent when she added. She should have written as .
She should have multiplied the exponents instead of adding them.
Bethany wants to estimate the value of . Which statement about the estimate is true? The value will be greater than 1 because is a very large number and multiplication always increases the size of a number. The value will be greater than 1 because and 8 is larger than 1. The value will be less than 1 because will be a negative number. All negative numbers are less than one. The number will be less than 1 because when adding the exponents, , and a number in scientific notation with a negative exponent is less than 1.
The number will be less than 1 because when adding the exponents, , and a number in scientific notation with a negative exponent is less than 1.
Annabelle measured her bedroom as 11 ft 13 ft, which is 143 square feet. She wants to change the units to square inches. Which statements should she consider when converting? Check all that apply. There are 12 inches in every foot. The length and width will increase by a factor of . The length and width will increase by a factor of . The area will increase by a factor of , since area is length times width. The area will increase by a factor of , since both the length and width increase by that factor. The area will increase by a factor of , since both the length and width increase by that factor. The area will increase by a factor of , since both the length and width increase by that factor.
There are 12 inches in every foot. The length and width will increase by a factor of . The area will increase by a factor of , since area is length times width.
Which equation finds the area of a square with a side length of 5n^4 units? square units square units square units square units
a
Which list is in order from least to greatest? , , , , , , , , , , , ,
a
Which list is in order from least to greatest? , , , , , , , , , , , ,
a 9.4x10^-8
Which expressions are equivalent to ? Check all that apply.
a b e
Geoffrey is evaluating the expression as shown below.What are the values of a, b, c, and d?
a=4 b=2 c=16 d=9
Which answer shows 0.05 written in scientific notation?
b
Which applies the power of a product rule to simplify (5t)^3
c
Dahlia is simplifying using these steps:Although Dahlia is correct so far, which step could she have used instead to simplify the expression ?
d
Mario simplified the expression as shown. Which statement explains Mario's error? He should have added the exponents instead of multiplying them. He should have subtracted the exponents instead of multiplying them. He should have applied the exponent -3 to 4, and not to z, to get . He should also have applied the exponent -3 to 4 to get .
d
Which expression can be simplified as 1/n^18
d
An inground swimming pool contains units of water. Which unit of measure was used? teaspoons cubic centimeters fluid ounces gallons
gallons
Which expression is equivalent to ? 13j
j^13
The simplified form of an expression is . Which expression was simplified?
not (256t^-7)^-4
Which number is written in scientific notation?
not 0.2x10^5
The quotient of and a number n results in . What is the value of n?
not 1.5x10^18
Which is the simplified form of the expression ?
not 1/6^42
What is the value of in scientific notation?
not 22.26 x 10^7
What is the value of in scientific notation?
not 22.26x 10^12
What is in scientific notation?
not 5.291 x 10^-64
What is in scientific notation?
not 5.291 x 10^20
Aliyah wants to estimate the value of the quotient of and . Which statement about the value is true? The value will be greater than 1 because is a positive number. A number in scientific notation with a positive exponent has a value greater than 1. The value will be greater than 1 because . A number in scientific notation with a positive exponent is greater than 1. The value will be less than 1 because is less than 1. The negative exponents will make it even smaller. The number will be less than 1 because is a very small number and division always makes the size of a number smaller.
not The number will be less than 1 because is a very small number and division always makes the size of a number smaller.
A jet flies at a rate of feet per hour. Written in scientific notation, which is the best estimate of how many feet the jet will travel in hours? feet feet feet feet
not a
Which answer shows 0.00897 written in scientific notation?
not a
A company produces light bulbs each week. Written in scientific notation, which is the best estimate of how many light bulbs the company will make in weeks? light bulbs light bulbs light bulbs light bulbs
not b
Ruchi measured the area of her kitchen as square units. When she recorded the area, she wrote square feet. Which statement about her labeling of the units is true? She is correct because dimensions of rooms must always be measured in feet and area would be square feet. She is correct because ft is equivalent to 2, 810 ft, which is an average size for a kitchen since area is always so much more than length. She is incorrect because is around 30,000 so the units must be smaller than feet. She most likely measured in inches. She is incorrect because 2.81 is a small number. She probably measured in yards to arrive at such a small value.
not b She is correct because ft is equivalent to 2, 810 ft, which is an average size for a kitchen since area is always so much more than length.
Which answer shows written in standard form? 0.000845 8,450 84,500 8,450,000
not d
Matsu wants to measure the dimensions of her vegetable garden. Which unit of measurement should she use to eliminate the need to write the values in scientific notation? inches feet cups tons
not inches
Loi used these steps to simplify the expression .Step 1:Subtract the exponents of powers with like bases.Step 2:Apply the power of a product rule.Step 3:Write negative exponents as reciprocals using positive exponents.Step 4:Evaluate the power with the integer base.In which step did Loi make the first error? Step 1 Step 2 Step 3 Step 4
not step 2
Which expression is equivalent to ? 9pq
pq^9
Which expression is equivalent to ?
q^12
Which rules of exponents will be used to evaluate this expression? Check all that apply. product of powers quotient of powers power of a power power of a product negative exponent zero exponent
quotient of powers power of a power negative exponent
Loi used these steps to simplify the expression .Step 1:Subtract the exponents of powers with like bases.Step 2:Apply the power of a product rule.Step 3:Write negative exponents as reciprocals using positive exponents.Step 4:Evaluate the power with the integer base.In which step did Loi make the first error? Step 1 Step 2 Step 3 Step 4
step 3
Tasha used the pattern in the table to find the value of .Powers of 4Value1641She used these steps.Step 1Find a pattern in the table.The pattern is to divide the previous value by 4 when the exponent decreases by 1.Step 2Find the value of .Step 3Find the value of .Step 4Rewrite the value for .In which step did Tasha make the first error? Step 1 Step 2 Step 3 Step 4
step 4
