Question

what is 6 to the power of -6 x 6 to the power of 2

Answer 1

To solve the expression \(6^{-6} \times 6^{2}\), we can use the properties of exponents.

When multiplying two expressions with the same base, we can add their exponents:

\[
6^{-6} \times 6^{2} = 6^{-6 + 2} = 6^{-4}
\]

Now, writing \(6^{-4}\) in positive exponent form gives us:

\[
6^{-4} = \frac{1}{6^{4}}
\]

Finally, \(6^{4}\) can be calculated as:

\[
6^{4} = 6 \times 6 \times 6 \times 6 = 1296
\]

Thus,

\[
6^{-4} = \frac{1}{1296}
\]

The final answer is:

\[
\frac{1}{1296}
\]