Basic Math Examples

${(\sqrt[5]{32})}^{- 3} \div 2^{4}$

Step 1

Rewrite the division as a fraction.

$\frac{{(\sqrt[5]{32})}^{- 3}}{2^{4}}$

Step 2

Move ${(\sqrt[5]{32})}^{- 3}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{2^{4} {\sqrt[5]{32}}^{3}}$

Step 3

Simplify the denominator.

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Step 3.1

Raise $2$ to the power of $4$ .

$\frac{1}{16 {\sqrt[5]{32}}^{3}}$

Step 3.2

Rewrite $32$ as $2^{5}$ .

$\frac{1}{16 {\sqrt[5]{2^{5}}}^{3}}$

Step 3.3

Pull terms out from under the radical, assuming real numbers.

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

Step 3.4

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

$\frac{1}{16 \cdot 8}$

Step 4

Multiply $16$ by $8$ .

$\frac{1}{128}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{128}$

Decimal Form:

$0.0078125$