Simplify the Radical Expression cube root of 4/(9m)

$\sqrt[3]{\frac{4}{9 m}}$

Rewrite $\sqrt[3]{\frac{4}{9 m}}$ as $\frac{\sqrt[3]{4}}{\sqrt[3]{9 m}}$ .

$\frac{\sqrt[3]{4}}{\sqrt[3]{9 m}}$

Multiply $\frac{\sqrt[3]{4}}{\sqrt[3]{9 m}}$ by $\frac{{\sqrt[3]{9 m}}^{2}}{{\sqrt[3]{9 m}}^{2}}$ .

$\frac{\sqrt[3]{4}}{\sqrt[3]{9 m}} \cdot \frac{{\sqrt[3]{9 m}}^{2}}{{\sqrt[3]{9 m}}^{2}}$

Combine and simplify the denominator.

Multiply $\frac{\sqrt[3]{4}}{\sqrt[3]{9 m}}$ by $\frac{{\sqrt[3]{9 m}}^{2}}{{\sqrt[3]{9 m}}^{2}}$ .

$\frac{\sqrt[3]{4} {\sqrt[3]{9 m}}^{2}}{\sqrt[3]{9 m} {\sqrt[3]{9 m}}^{2}}$

Raise $\sqrt[3]{9 m}$ to the power of $1$ .

$\frac{\sqrt[3]{4} {\sqrt[3]{9 m}}^{2}}{{\sqrt[3]{9 m}}^{1} {\sqrt[3]{9 m}}^{2}}$

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

$\frac{\sqrt[3]{4} {\sqrt[3]{9 m}}^{2}}{{\sqrt[3]{9 m}}^{1 + 2}}$

Add $1$ and $2$ .

$\frac{\sqrt[3]{4} {\sqrt[3]{9 m}}^{2}}{{\sqrt[3]{9 m}}^{3}}$

Rewrite ${\sqrt[3]{9 m}}^{3}$ as $9 m$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{9 m}$ as ${(9 m)}^{\frac{1}{3}}$ .

$\frac{\sqrt[3]{4} {\sqrt[3]{9 m}}^{2}}{{({(9 m)}^{\frac{1}{3}})}^{3}}$

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

$\frac{\sqrt[3]{4} {\sqrt[3]{9 m}}^{2}}{{(9 m)}^{\frac{1}{3} \cdot 3}}$

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

$\frac{\sqrt[3]{4} {\sqrt[3]{9 m}}^{2}}{{(9 m)}^{\frac{3}{3}}}$

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{\sqrt[3]{4} {\sqrt[3]{9 m}}^{2}}{{(9 m)}^{\frac{3}{3}}}$

Rewrite the expression.

$\frac{\sqrt[3]{4} {\sqrt[3]{9 m}}^{2}}{{(9 m)}^{1}}$

Simplify.

$\frac{\sqrt[3]{4} {\sqrt[3]{9 m}}^{2}}{9 m}$

Simplify the numerator.

Rewrite ${\sqrt[3]{9 m}}^{2}$ as ${({(9 m)}^{2})}^{\frac{1}{3}}$ .

$\frac{\sqrt[3]{4} \sqrt[3]{{(9 m)}^{2}}}{9 m}$

Apply the product rule to $9 m$ .

$\frac{\sqrt[3]{4} \sqrt[3]{9^{2} m^{2}}}{9 m}$

Raise $9$ to the power of $2$ .

$\frac{\sqrt[3]{4} \sqrt[3]{81 m^{2}}}{9 m}$

Rewrite $81 m^{2}$ as $3^{3} \cdot (3 m^{2})$ .

Factor $27$ out of $81$ .

$\frac{\sqrt[3]{4} \sqrt[3]{27 (3) m^{2}}}{9 m}$

Rewrite $27$ as $3^{3}$ .

$\frac{\sqrt[3]{4} \sqrt[3]{3^{3} \cdot 3 m^{2}}}{9 m}$

Add parentheses.

$\frac{\sqrt[3]{4} \sqrt[3]{3^{3} \cdot (3 m^{2})}}{9 m}$

Pull terms out from under the radical.

$\frac{\sqrt[3]{4} \cdot 3 \sqrt[3]{3 m^{2}}}{9 m}$

Combine exponents.

Combine using the product rule for radicals.

$\frac{3 \sqrt[3]{4 (3 m^{2})}}{9 m}$

Multiply $4$ by $3$ .

$\frac{3 \sqrt[3]{12 m^{2}}}{9 m}$

Cancel the common factor of $3$ and $9$ .

Factor $3$ out of $3 \sqrt[3]{12 m^{2}}$ .

$\frac{3 (\sqrt[3]{12 m^{2}})}{9 m}$

Cancel the common factors.

Factor $3$ out of $9 m$ .

$\frac{3 (\sqrt[3]{12 m^{2}})}{3 (3 m)}$

Cancel the common factor.

$\frac{3 \sqrt[3]{12 m^{2}}}{3 (3 m)}$

Rewrite the expression.

$\frac{\sqrt[3]{12 m^{2}}}{3 m}$

Simplify the Radical Expression cube root of 4/(9m)

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