Algebra Examples

$64^{\frac{- 1}{2}}$

Step 1

Move the negative in front of the fraction.

$64^{- \frac{1}{2}}$

Step 2

Rewrite the expression using the negative exponent rule

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

$\frac{1}{64^{\frac{1}{2}}}$

Step 3

Simplify the denominator.

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Step 3.1

Rewrite

$64$ as

$8^{2}$ .

$\frac{1}{{(8^{2})}^{\frac{1}{2}}}$

Step 3.2

Apply the power rule and multiply exponents,

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

$\frac{1}{8^{2 (\frac{1}{2})}}$

Step 3.3

Cancel the common factor of

$2$ .

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Step 3.3.1

Cancel the common factor.

$\frac{1}{8^{2 (\frac{1}{2})}}$

Step 3.3.2

Rewrite the expression.

$\frac{1}{8^{1}}$

$\frac{1}{8^{1}}$

Step 3.4

Evaluate the exponent.

$\frac{1}{8}$

$\frac{1}{8}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{8}$

Decimal Form:

$0.125$

$64^{\frac{- 1}{2}}$

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