Question - Simplifying a Fraction with Exponents

Given the expression:

\[\frac{10^{-8}}{7^5 \times 10^3 \times 7^{-7}}\]

We can rewrite the denominator:

\(7^5 \times 10^3 \times 7^{-7} = 10^3 \times 7^{5 - 7} = 10^3 \times 7^{-2}\)

Next, we place this back into the expression:

\[\frac{10^{-8}}{10^3 \times 7^{-2}} = \frac{10^{-8}}{10^3} \times 7^2\]

Simplifying \(\frac{10^{-8}}{10^3}\):

\(10^{-8 - 3} = 10^{-11}\)

The expression becomes:

\(10^{-11} \times 7^2\)

Thus, the final simplified expression is:

\[7^2 \times 10^{-11}\]

Which can be written as:

\(49 \times 10^{-11}\)