algebra 1a - unit 1: the real numbers
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
