Question

Write the expression with positive exponents only. Then​ simplify, if possible.
StartFraction 1 Over left parenthesis negative 10 right parenthesis Superscript negative 2 EndFraction
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Part 1
StartFraction 1 Over left parenthesis negative 10 right parenthesis Superscript negative 2 EndFraction
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Answer 1

To rewrite the expression \(\frac{1}{(-10)^{-2}}\) with positive exponents, we can apply the property of exponents that states \(a^{-n} = \frac{1}{a^n}\), which also implies that \(\frac{1}{a^{-n}} = a^n\).

Starting with the original expression:

\[
\frac{1}{(-10)^{-2}}
\]

We can rewrite it as follows:

\[
(-10)^{2}
\]

Now, simplifying \((-10)^{2}\):

\[
(-10)^{2} = 100
\]

Thus, the expression simplifies to:

\[
100
\]

So, the final result is:

\[
\frac{1}{(-10)^{-2}} = 100
\]