Question

Which of the following is equal to the expression below?
(5^-6) ^2

A. -5^12
B. 1/5^4
C.1/5^12
D. -5^4

Answer 1

To simplify the expression \((5^{-6})^2\), we can use the exponentiation property \((a^m)^n = a^{m \cdot n}\).

So, we have:
\[
(5^{-6})^2 = 5^{-6 \cdot 2} = 5^{-12}
\]

The expression \(5^{-12}\) can be rewritten as:
\[
5^{-12} = \frac{1}{5^{12}}
\]

Now, looking at the options provided:

A. \(-5^{12}\)

B. \(\frac{1}{5^4}\)

C. \(\frac{1}{5^{12}}\)

D. \(-5^4\)

The correct answer, as we derived, is:
\[
\frac{1}{5^{12}}
\]
Thus, the correct answer is **C. \(\frac{1}{5^{12}}\)**.