Algebra Examples

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

$16^{- \frac{1}{2}}$

Step 1

Rewrite the expression using the negative exponent rule

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

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

\frac{1}{16^{\frac{1}{2}}}

$\frac{1}{16^{\frac{1}{2}}}$

Step 2

Simplify the denominator.

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Step 2.1

Rewrite

16

$16$ as

4^{2}

$4^{2}$ .

\frac{1}{{(4^{2})}^{\frac{1}{2}}}

$\frac{1}{{(4^{2})}^{\frac{1}{2}}}$

Step 2.2

Apply the power rule and multiply exponents,

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

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

\frac{1}{4^{2 (\frac{1}{2})}}

$\frac{1}{4^{2 (\frac{1}{2})}}$

Step 2.3

Cancel the common factor of

2

$2$ .

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Step 2.3.1

Cancel the common factor.

$\frac{1}{4^{2 (\frac{1}{2})}}$

Step 2.3.2

Rewrite the expression.

$\frac{1}{4^{1}}$

$\frac{1}{4^{1}}$

Step 2.4

Evaluate the exponent.

$\frac{1}{4}$

$\frac{1}{4}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{4}$

Decimal Form:

$0.25$

$16^{- \frac{1}{2}}$

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