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: \[ \frac{1}{46656} \]