Question

Use the rules of exponents to simplify the following expression and remove all zero and negative exponents. Assume that all variables are nonzero.
left parenthesis 5 Superscript negative 1 Baseline right parenthesis squared
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Part 1
left parenthesis 5 Superscript negative 1 Baseline right parenthesis squaredequals
  
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​(Type an integer or a​ fraction.)

Answer 1

To simplify the expression \((5^{-1})^2\), we can apply the rule of exponents which states that \((a^m)^n = a^{m \cdot n}\).

Applying this rule:

\[
(5^{-1})^2 = 5^{-1 \cdot 2} = 5^{-2}
\]

Now, to remove the negative exponent, we use the fact that \(a^{-n} = \frac{1}{a^n}\):

\[
5^{-2} = \frac{1}{5^2}
\]

Calculating \(5^2\):

\[
5^2 = 25
\]

So,

\[
5^{-2} = \frac{1}{25}
\]

Thus, the final simplified expression is:

\[
(5^{-1})^2 = \frac{1}{25}
\]