Select the equivalent expression.

Question

\[\dfrac{1}{6^{5}}=?\]
Choose 1 answer:
Choose 1 answer:
(Choice A)

\[6^{^{\frac1{5}}}\]
A

\[6^{^{\frac1{5}}}\]
(Choice B)

\[\dfrac{1^{5}}{6}\]
B

\[\dfrac{1^{5}}{6}\]
(Choice C)
\[6^{-{5}}\]
C
\[6^{-{5}}\]

Answer 1

To find the equivalent expression for \(\dfrac{1}{6^{5}}\), we can use the property of exponents which states that \(\dfrac{1}{a^b} = a^{-b}\).

Applying this property here:

\[ \dfrac{1}{6^{5}} = 6^{-5} \]

Now let's compare this with the given choices:

• (Choice A) \(6^{\frac{1}{5}}\) - This is not equivalent.
• (Choice B) \(\dfrac{1^{5}}{6}\) - This simplifies to \(\dfrac{1}{6}\), which is also not equivalent.
• (Choice C) \(6^{-5}\) - This is equivalent to our expression.

Thus, the correct choice is:

Choice C: \(6^{-5}\)