Simplify ( cube root of 6)/( cube root of 32)

$\frac{\sqrt[3]{6}}{\sqrt[3]{32}}$

Combine $\sqrt[3]{6}$ and $\sqrt[3]{32}$ into a single radical.

$\sqrt[3]{\frac{6}{32}}$

Cancel the common factor of $6$ and $32$ .

Factor $2$ out of $6$ .

$\sqrt[3]{\frac{2 (3)}{32}}$

Cancel the common factors.

Factor $2$ out of $32$ .

$\sqrt[3]{\frac{2 \cdot 3}{2 \cdot 16}}$

Cancel the common factor.

$\sqrt[3]{\frac{2 \cdot 3}{2 \cdot 16}}$

Rewrite the expression.

$\sqrt[3]{\frac{3}{16}}$

Rewrite $\sqrt[3]{\frac{3}{16}}$ as $\frac{\sqrt[3]{3}}{\sqrt[3]{16}}$ .

$\frac{\sqrt[3]{3}}{\sqrt[3]{16}}$

Simplify the denominator.

Rewrite $16$ as $2^{3} \cdot 2$ .

Factor $8$ out of $16$ .

$\frac{\sqrt[3]{3}}{\sqrt[3]{8 (2)}}$

Rewrite $8$ as $2^{3}$ .

$\frac{\sqrt[3]{3}}{\sqrt[3]{2^{3} \cdot 2}}$

Pull terms out from under the radical.

$\frac{\sqrt[3]{3}}{2 \sqrt[3]{2}}$

Multiply $\frac{\sqrt[3]{3}}{2 \sqrt[3]{2}}$ by $\frac{{\sqrt[3]{2}}^{2}}{{\sqrt[3]{2}}^{2}}$ .

$\frac{\sqrt[3]{3}}{2 \sqrt[3]{2}} \cdot \frac{{\sqrt[3]{2}}^{2}}{{\sqrt[3]{2}}^{2}}$

Combine and simplify the denominator.

Multiply $\frac{\sqrt[3]{3}}{2 \sqrt[3]{2}}$ by $\frac{{\sqrt[3]{2}}^{2}}{{\sqrt[3]{2}}^{2}}$ .

$\frac{\sqrt[3]{3} {\sqrt[3]{2}}^{2}}{2 \sqrt[3]{2} {\sqrt[3]{2}}^{2}}$

Move $\sqrt[3]{2}$ .

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

Raise $\sqrt[3]{2}$ to the power of $1$ .

$\frac{\sqrt[3]{3} {\sqrt[3]{2}}^{2}}{2 ({\sqrt[3]{2}}^{1} {\sqrt[3]{2}}^{2})}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Add $1$ and $2$ .

$\frac{\sqrt[3]{3} {\sqrt[3]{2}}^{2}}{2 {\sqrt[3]{2}}^{3}}$

Rewrite ${\sqrt[3]{2}}^{3}$ as $2$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{2}$ as $2^{\frac{1}{3}}$ .

$\frac{\sqrt[3]{3} {\sqrt[3]{2}}^{2}}{2 {(2^{\frac{1}{3}})}^{3}}$

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

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

Combine $\frac{1}{3}$ and $3$ .

$\frac{\sqrt[3]{3} {\sqrt[3]{2}}^{2}}{2 \cdot 2^{\frac{3}{3}}}$

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{\sqrt[3]{3} {\sqrt[3]{2}}^{2}}{2 \cdot 2^{\frac{3}{3}}}$

Rewrite the expression.

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

Evaluate the exponent.

$\frac{\sqrt[3]{3} {\sqrt[3]{2}}^{2}}{2 \cdot 2}$

Simplify the numerator.

Rewrite ${\sqrt[3]{2}}^{2}$ as ${(2^{2})}^{\frac{1}{3}}$ .

$\frac{\sqrt[3]{3} \sqrt[3]{2^{2}}}{2 \cdot 2}$

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

$\frac{\sqrt[3]{3} \sqrt[3]{4}}{2 \cdot 2}$

Multiply $2$ by $2$ .

$\frac{\sqrt[3]{3} \sqrt[3]{4}}{4}$

Simplify the numerator.

Combine using the product rule for radicals.

$\frac{\sqrt[3]{3 \cdot 4}}{4}$

Multiply $3$ by $4$ .

$\frac{\sqrt[3]{12}}{4}$

The result can be shown in multiple forms.

Exact Form:

$\frac{\sqrt[3]{12}}{4}$

Decimal Form:

$0.57235712 \dots$

Simplify ( cube root of 6)/( cube root of 32)

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