Select the equivalent expression.

Question

\[\left(\dfrac{x^{4}}{7^{-8}}\right)^{-7}=?\]
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) \({x^{-28}}\cdot{7^{-56}}\).