Algebra Examples

25^{- \frac{3}{2}}

$25^{- \frac{3}{2}}$

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{3}{2}}}

$\frac{1}{25^{\frac{3}{2}}}$

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{3}{2}}}

$\frac{1}{{(5^{2})}^{\frac{3}{2}}}$

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{3}{2})}}

$\frac{1}{5^{2 (\frac{3}{2})}}$

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{3}{2})}}

$\frac{1}{5^{2 (\frac{3}{2})}}$

Step 2.3.2

Rewrite the expression.

\frac{1}{5^{3}}

$\frac{1}{5^{3}}$

\frac{1}{5^{3}}

$\frac{1}{5^{3}}$

Step 2.4

Raise

5

$5$ to the power of

3

$3$ .

\frac{1}{125}

$\frac{1}{125}$

\frac{1}{125}

$\frac{1}{125}$

Step 3

The result can be shown in multiple forms.

Exact Form:

\frac{1}{125}

$\frac{1}{125}$

Decimal Form:

0.008

$0.008$

[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$