Question

Chris tried to rewrite the expression \left( 4^{-2} \cdot 4^{-3} \right)^{3}(4

−2

⋅4

−3

)

3

left parenthesis, 4, start superscript, minus, 2, end superscript, dot, 4, start superscript, minus, 3, end superscript, right parenthesis, cubed.

\begin{aligned} &\phantom{=}\left( 4^{-2} \cdot 4^{-3} \right)^{3} \\\\ &=\left( 4^{-5} \right)^{3}&\text{Step } 1 \\\\ &=4^{-2}&\text{Step } 2 \\\\ &=\dfrac{1}{4^{2}}&\text{Step } 3 \end{aligned}

​


=(4

−2

⋅4

−3

)

3


=(4

−5

)

3


=4

−2


=

4

2


1

​


​


Step 1

Step 2

Step 3

​


Did Chris make a mistake? If so, in which step?

Choose 1 answer:

Choose 1 answer:


(Choice A)

A

Chris did not make a mistake.


(Choice B)

B

Chris made a mistake in Step 1.


(Choice C)

C

Chris made a mistake in Step 2.


(Choice D)

D

Chris made a mistake in Step 3.

Answer 1

We have been given an expression
`\left( 4^(-2) \cdot 4^(-3) \right)^(3)`. We have been given steps how Chris tried to solve the given expression. We are asked to choose the correct option about Chris's work.

Let us simplify our given expression.

Using exponent property,
`a^m\cdot a^n=a^(m+n)`, we cab rewrite our given expression as:

`\left( 4^(-2+(-3)) \right)^(3)`

`\left( 4^(-5) \right)^(3)`

Now we will use exponent property
`(a^m)^n=a^(m\cdot n)`to further simplify our expression.

`\left( 4^(-5) \right)^(3)= 4^(-5\cdot 3)`

`\left( 4^(-5) \right)^(3)= 4^(-15)`

Therefore, Chris made mistake in step 2.