algebra 1a - unit 1: the real numbers

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simplify. (-5)^5/(-5)^-6

(-5)^11

which expressions are equal to 1? select all that apply.

(1/3)^0 1291^0 (-0.0008)^0

which expression is equivalent to (4^1/3•4^2/6///4^5/6)^3/11?

(1/4)^3/66

which expressions are equivalent to √5^1/2•4///2•5^1/3?

(1/5)^1/12 12√1/5 5^-1/12 12√5^-1

find the equivalent for -(3)^-4

-(1/3 • 1/3 • 1/3 • 1/3)

what is the value of the expression 4^1/2 • 2/4√16 - 10 \ 2?

-3

what is the value of the expression 6^2/3//18^1/3 \ 2^1/3 - 1?

0

what is the value of the expression (8√81)^2 \ (2^3)^1/2///2^1/2 - 1 \ 2?

1

what is the value of the expression 3^1/2 • 8√3//2 \ 6 - 1?

1

which number equals (5)^-3?

1/125

rewrite the expression (3^3/4///3^3/8)^4/9 as an exponent with a single base, 3^x. what is the value of x?

1/6

which expression is equivalent to 5√11^3?

11^3/5

suppose 12 is raised to the second power, like this: 12^2. which answers show the inverse operation?

12^1/2 √12

which expression is equivalent to (12^4)^2/9?

12^8/9

which number equals (3/4)^-2?

16/9

which expressions are equivalent to (18^5)^3/8?select all that apply.

18^15/8 18^5•3/8 18^5/1*3/8

evaluate 32^1/5

2

what is the value of 12√8^4?

2

which expression is equivalent to 243^1/10 \ (3^4)^1/2///3^1/2 - 1 \ 5?

2/15

evaluate the expression 3√125^2

25

how can (√25)^2 be rewritten? select all that apply.

25 5^2

simplify. 26 • 26^8

26^9

which expression is equivalent to (2^3 • 9)^4/5?

2^12/5 • 9^4/5

which expressions are equivalent to 3√8^1/33//32^1/9?

2^2/9 * 3^-2/3 (9√2)^2 * (3√1/3)^2 9√4 * 3√1/9 9√2^2 * 3√3^-2

which expression is equivalent to (2^7 • 3^-5 • 9)^4?

2^28 • 3^-20 • 9^4

which expression is equivalent to 7√2^3?

2^3/7

which expressions are equivalent to 2^2/7 • 2^2/7? select all that apply.

2^4/7 2^2/7+2/7

which expression is equivalent to (2/7)^5?

2^5/7^5

which expression is equivalent to √116?

2√29

what is the index when x^2/3 is rewritten as a radical expression?

3

evaluate 3√27/125

3/5

which answer is equivalent to (5^-2 * 9)/(2^4 * 4^-3)?

36/25

which of the following is equivalent to 3^-8 • 3^4?

3^-4

which expressions are equivalent to 3^4/9 / 3^2/9? select all that apply.

3^2/9 3^4/9-2/9

which expressions are equivalent to 27^1/3 • 3/9^1/3 - 18 \ 6?

3^4/3 - 3 (3√3)^4 - 3

which expression correctly simplifies (3^1/2///4^1/5)^5/6?

3^5/12 //// 4^1/6

which of the following is equivalent to x^2/3 / y^-3/4?

3√x^2 • 4√y^3

evaluate the radical expression 4√256

4

which expression correctly simplifies 4^3/4 / 4^1/5? select all that apply.

4^11/20

which expression is equivalent to (4^-3)^-6?

4^18

how can the expression √112 be correctly rewritten?

4√7

which radical expressions are equivalent to 7^5/4? select all that apply.

4√7^5 (4√7)^5

delcie is asked to rewrite the expression 3√500 using an exponent. how should delcie correctly rewrite the expression?

500^1/3

what is the value of the expression 2/6√8 • √2 - (-18/√81 - 2)?

6

what is the value of the expression 27^1/3/√4 - 3 • 6^-1 + 4√625?

6

which expression is equivalent to 6^3/10 /// 6^1/5?

6^1/10

which expression is equivalent 6^3 • 6^1/4?

6^13/4

evaluate (49/64)^1/2

7/8

what is the value of the expression √2 • 8√2/3 \ 3 - 1?

7/9

which expressions are equivalent to (6^2/7^3)^-4?

7^12/6^8 6^-8/7^-12

which value is equivalent to 7^-3/7^-5?

7^2

what is the value of 128^3/7?

8

which number is equivalent to (1/3)^-4?

81

simplify. 8^15 / 8^-3

8^18

choose the equivalent expression. (8^10)^2

8^20

simply the following expression. 9^-53 • 9^37

9^-16

which expression is equivalent to (9 • 5)^2/3?

9^2/3 • 5^2/3

which expression is equivalent to (9 • 8)^4?

9^4 • 8^4

the difference of a rational number and an irrational number is ____ an irrational number.

always

which expressions are equivalent to a^b/c? select all that apply.

c√a^b (c√a)^b

what is the radical expression that is equivalent to 27^1/5?

fifthroot(27) copy every word for the point.

jacob says that the product of a rational number and an irrational number is sometimes rational and sometimes irrational. which statement correct describes whether jacob is correct or incorrect?

jacob is correct; the product of a rational number and an irrational number may be either rational or irrational

the difference of a rational number and an irrational number is ___ a rational number.

never

lindsey simplified the radical expression √50 as shown. step 1: √5•5•2 step 2: √5^2 • √2 step 3: 5√2 did lindsey make a mistake?

no, all of her work is correct.

lesson 5

order of operations

lesson 4

performing operations with irrational numbers

lesson 1

properties of integer exponents

lesson 3

properties of rational exponents

lesson 2

radicals and rational exponents

the product of a rational number and an irrational number is ___ an irrational number.

sometimes

the product of two irrational numbers is ___ an irrational number.

sometimes

the sum of two irrational numbers is ____ a rational number.

sometimes

sunny states that the product of two irrational numbers is always irrational. which statement correctly describes whether sunny is correct or incorrect?

sunny is incorrect; the product of two irrational numbers may be either rational or irrational

which explanation correctly analyzes the difference between an irrational number and a rational number?

the expression √25 - √21 can be rewritten as 5 - √21. since the exact value of √21 cannot be found, the difference is irrational.

sunny simplified the expression (3√4^3)^1/2 as shown. did sunny make a mistake?

yes, in step 1, he should have written 4 instead of √4. his final answer should have been 4^1/2, or √4.

select all numbers that are irrational.

√0.156 14.19274128 . . . 368.5468432 . . .

which expression is equivalent to √48/175?

√2•2•2•2•3/5•5•7 read closely!

which expression is equivalent to √180?

√2•2•3•3•5

match each radical expression with the equivalent exponential expression.

√3 : 3^1/2 3√2 : 2^1/3 4√3 : 3^1/4 5√2 : 2^1/5

match each irrational number with another irrational number so that the product of the two numbers is rational.

√6 : √6 √3 : √12 √2 : √32 √20 : √5


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