Basic Math Examples

25^{- \frac{1}{2}}

$25^{- \frac{1}{2}}$

Step 1

Rewrite the expression using the negative exponent rule

b^{- n} = \frac{1}{b^{n}}

$b^{- n} = \frac{1}{b^{n}}$ .

\frac{1}{25^{\frac{1}{2}}}

$\frac{1}{25^{\frac{1}{2}}}$

Step 2

Simplify the denominator.

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Step 2.1

Rewrite

25

$25$ as

5^{2}

$5^{2}$ .

\frac{1}{{(5^{2})}^{\frac{1}{2}}}

$\frac{1}{{(5^{2})}^{\frac{1}{2}}}$

Step 2.2

Apply the power rule and multiply exponents,

{(a^{m})}^{n} = a^{m n}

${(a^{m})}^{n} = a^{m n}$ .

\frac{1}{5^{2 (\frac{1}{2})}}

$\frac{1}{5^{2 (\frac{1}{2})}}$

Step 2.3

Cancel the common factor of

2

$2$ .

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Step 2.3.1

Cancel the common factor.

\frac{1}{5^{2 (\frac{1}{2})}}

$\frac{1}{5^{2 (\frac{1}{2})}}$

Step 2.3.2

Rewrite the expression.

\frac{1}{5^{1}}

$\frac{1}{5^{1}}$

\frac{1}{5^{1}}

$\frac{1}{5^{1}}$

Step 2.4

Evaluate the exponent.

\frac{1}{5}

$\frac{1}{5}$

\frac{1}{5}

$\frac{1}{5}$

Step 3

The result can be shown in multiple forms.

Exact Form:

\frac{1}{5}

$\frac{1}{5}$

Decimal Form:

0.2

$0.2$