Question

(1/6^2)^3

Answer 1

To simplify \((1/6^2)^3\), we can break it down step by step.

First, calculate \(6^2\):
\[
6^2 = 36
\]

Now, substituting that into the expression gives:
\[
(1/36)^3
\]

Next, we raise \(\frac{1}{36}\) to the power of 3:
\[
(1/36)^3 = \frac{1^3}{36^3} = \frac{1}{36^3}
\]

Now, calculate \(36^3\):
\[
36^3 = 36 \times 36 \times 36
\]
Calculating \(36 \times 36\):
\[
36 \times 36 = 1296
\]

Now multiply \(1296\) by \(36\):
\[
1296 \times 36 = 46656
\]

So, \(36^3 = 46656\). This gives us:
\[
(1/6^2)^3 = \frac{1}{46656}
\]

Thus, the final answer is:
\[
\frac{1}{46656}
\]