AnswersAG Q1 Keystone Algebra 1 Block 26-27 DDiamondRaising a Power to a Power

Evaluating Expressions with Exponents Answers

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1
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Fatima evaluated the expression , when and . Her work is shown below. What was Fatima’s error?

Question illustration
A
She subtracted the exponents incorrectly when simplifying the expression.
B
She substituted the wrong values for the variables.
C
She did not correctly follow the order of operations by applying the exponent to .
Option C
D
She found an incorrect value for since the value should be negative.
Option D
2
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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?

Question illustration
A
Nadine is incorrect because she should have applied the quotient of powers rule first.
B
Nadine is correct because she correctly applied the power of a product rule.
C
Calvin is incorrect because he should have applied the power of a product rule first.
D
Calvin is correct because he correctly applied the quotient of powers rule.
3

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?

Question illustration
A
Step 1
B
Step 2
C
Step 3
D
Step 4
4

Which is the value of this expression when and ?

Question illustration
A
StartFraction 4 Over 9 EndFraction
Option A
B
StartFraction 27 Over 8 EndFraction
Option B
C
StartFraction 243 Over 32 EndFraction
Option C
D
StartFraction 729 Over 64 EndFraction
Option D
5

Which is the value of this expression when and ?

Question illustration
A
StartFraction 1 Over 75 EndFraction
Option A
B
StartFraction 9 Over 25 EndFraction
Option B
C
StartFraction 25 Over 9 EndFraction
Option C
D
75
6

Which shows how to find the value of this expression when and ?

Question illustration
A
StartFraction 3 squared (negative 2) Superscript 6 Baseline Over 5 Superscript 4 EndFraction
Option A
B
StartFraction 3 (negative 2) Superscript 6 Baseline Over 5 Superscript 4 EndFraction
Option B
C
StartFraction 3 squared (5 Superscript 6 Baseline) Over (negative 2) Superscript negative 4 Baseline EndFraction
Option C
D
StartFraction 3 Over (2) Superscript 6 Baseline 5 Superscript 4 Baseline EndFraction
Option D
7

Which is the simplified form of the expression ?

Question illustration
A
StartFraction 1 Over q Superscript 30 Baseline EndFraction
Option A
B
q Superscript 30
Option B
C
StartFraction p Superscript 12 Baseline Over q Superscript 60 Baseline EndFraction
Option C
D
p Superscript 12 Baseline q Superscript 60
Option D
8

Which is the simplified form of the expression ?

Question illustration
A
StartFraction 1 Over 6 Superscript 42 Baseline EndFraction
Option A
B
StartFraction 1 Over 6 Superscript 19 Baseline EndFraction
Option B
C
6 Superscript 6
Option C
D
6 Superscript 30
Option D
9

Which is the value of this expression when and ?

Question illustration
A
–4
B
Negative StartFraction 1 Over 16 EndFraction
Option B
C
StartFraction 1 Over 16 EndFraction
Option C
D
4
10

Which is the simplified form of the expression ?

Question illustration
A
StartFraction 1 Over 4 x squared y Superscript 16 Baseline EndFraction
Option A
B
StartFraction 4 Over x squared y Superscript 16 Baseline EndFraction
Option B
C
StartFraction 1 Over 4 x Superscript 14 y Superscript 8 Baseline EndFraction
Option C
D
StartFraction 4 Over x Superscript 14 Baseline y Superscript 8 Baseline EndFraction
Option D

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