Evaluate ( fifth root of 243/32)^3

${(\sqrt[5]{\frac{243}{32}})}^{3}$

Rewrite $\sqrt[5]{\frac{243}{32}}$ as $\frac{\sqrt[5]{243}}{\sqrt[5]{32}}$ .

${(\frac{\sqrt[5]{243}}{\sqrt[5]{32}})}^{3}$

Simplify the numerator.

Rewrite $243$ as $3^{5}$ .

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

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

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

Simplify the denominator.

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

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

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

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

Simplify the expression.

Apply the product rule to $\frac{3}{2}$ .

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

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

$\frac{27}{2^{3}}$

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

$\frac{27}{8}$

The result can be shown in multiple forms.

Exact Form:

$\frac{27}{8}$

Decimal Form:

$3.375$

Mixed Number Form:

$3 \frac{3}{8}$