Algebra Examples

$4^{- \frac{3}{2}}$

Step 1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{4^{\frac{3}{2}}}$

Step 2

Simplify the denominator.

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Step 2.1

Rewrite $4$ as $2^{2}$ .

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

Step 2.2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

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

Step 2.3

Cancel the common factor of $2$ .

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Step 2.3.1

Cancel the common factor.

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

Step 2.3.2

Rewrite the expression.

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

Step 2.4

Raise $2$ to the power of $3$ .

$\frac{1}{8}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{8}$

Decimal Form:

$0.125$