Algebra Examples

$16^{\frac{- 3}{2}}$

Step 1

Move the negative in front of the fraction.

$16^{- \frac{3}{2}}$

Step 2

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

$\frac{1}{16^{\frac{3}{2}}}$

Step 3

Simplify the denominator.

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Step 3.1

Rewrite $16$ as $4^{2}$ .

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

Step 3.2

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

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

Step 3.3

Cancel the common factor of $2$ .

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Step 3.3.1

Cancel the common factor.

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

Step 3.3.2

Rewrite the expression.

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

Step 3.4

Raise $4$ to the power of $3$ .

$\frac{1}{64}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{64}$

Decimal Form:

$0.015625$