Question

Select the equivalent expression.

\[\left(\dfrac{x^{4}}{7^{-8}}\right)^{-7}=?\]
Choose 1 answer:
Choose 1 answer:
(Choice A)
\[{x^{-28}}\cdot{7^{-56}}\]
A
\[{x^{-28}}\cdot{7^{-56}}\]
(Choice B)

\[\dfrac{x^{28}}{7^{-56}}\]
B

\[\dfrac{x^{28}}{7^{-56}}\]
(Choice C)

\[\dfrac{x^{28}}{7^{56}}\]
C

\[\dfrac{x^{28}}{7^{56}}\]

Answer 1

To simplify the expression \(\left(\dfrac{x^{4}}{7^{-8}}\right)^{-7}\), we can follow these steps:

1. Rewrite the expression:
\[
\left(\dfrac{x^{4}}{7^{-8}}\right)^{-7} = \left(x^{4} \cdot 7^{8}\right)^{-7}
\]
(Note that \( \dfrac{1}{7^{-8}} = 7^{8} \)).

2. Apply the exponent \(-7\) to both parts:
\[
\left(x^{4}\right)^{-7} \cdot \left(7^{8}\right)^{-7} = x^{-28} \cdot 7^{-56}
\]

Thus, the simplified expression is:
\[
x^{-28} \cdot 7^{-56}
\]

Now, looking at the choices:

- (Choice A) \({x^{-28}}\cdot{7^{-56}}\): **This is correct.**
- (Choice B) \(\dfrac{x^{28}}{7^{-56}}\): **This is not correct.**
- (Choice C) \(\dfrac{x^{28}}{7^{56}}\): **This is not correct.**

Therefore, the answer is **(Choice A) \({x^{-28}}\cdot{7^{-56}}\)**.