Question

Which expression is equivalent to left parenthesis, 5, to the power 6 , right parenthesis, to the power minus 5 , question mark(5
6
)
−5
?

Answer 1

To simplify the expression \( (5^6)^{-5} \), we can use the power of a power property of exponents, which states that \( (a^m)^n = a^{m \cdot n} \).

Applying this to our expression:

\[
(5^6)^{-5} = 5^{6 \cdot (-5)}
\]

Now, we calculate \( 6 \cdot (-5) \):

\[
6 \cdot (-5) = -30
\]

So we have:

\[
(5^6)^{-5} = 5^{-30}
\]

Thus, the expression \( (5^6)^{-5} \) is equivalent to \( 5^{-30} \).