Write the Fraction in Simplest Form ( cube root of 9)/( cube root of 11)

$\frac{\sqrt[3]{9}}{\sqrt[3]{11}}$

Step 1

Multiply $\frac{\sqrt[3]{9}}{\sqrt[3]{11}}$ by $\frac{{\sqrt[3]{11}}^{2}}{{\sqrt[3]{11}}^{2}}$ .

$\frac{\sqrt[3]{9}}{\sqrt[3]{11}} \cdot \frac{{\sqrt[3]{11}}^{2}}{{\sqrt[3]{11}}^{2}}$

Step 2

Combine and simplify the denominator.

Multiply $\frac{\sqrt[3]{9}}{\sqrt[3]{11}}$ by $\frac{{\sqrt[3]{11}}^{2}}{{\sqrt[3]{11}}^{2}}$ .

$\frac{\sqrt[3]{9} {\sqrt[3]{11}}^{2}}{\sqrt[3]{11} {\sqrt[3]{11}}^{2}}$

Raise $\sqrt[3]{11}$ to the power of $1$ .

$\frac{\sqrt[3]{9} {\sqrt[3]{11}}^{2}}{{\sqrt[3]{11}}^{1} {\sqrt[3]{11}}^{2}}$

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

$\frac{\sqrt[3]{9} {\sqrt[3]{11}}^{2}}{{\sqrt[3]{11}}^{1 + 2}}$

Add $1$ and $2$ .

$\frac{\sqrt[3]{9} {\sqrt[3]{11}}^{2}}{{\sqrt[3]{11}}^{3}}$

Rewrite ${\sqrt[3]{11}}^{3}$ as $11$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{11}$ as $11^{\frac{1}{3}}$ .

$\frac{\sqrt[3]{9} {\sqrt[3]{11}}^{2}}{{(11^{\frac{1}{3}})}^{3}}$

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

$\frac{\sqrt[3]{9} {\sqrt[3]{11}}^{2}}{11^{\frac{1}{3} \cdot 3}}$

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

$\frac{\sqrt[3]{9} {\sqrt[3]{11}}^{2}}{11^{\frac{3}{3}}}$

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{\sqrt[3]{9} {\sqrt[3]{11}}^{2}}{11^{\frac{3}{3}}}$

Rewrite the expression.

$\frac{\sqrt[3]{9} {\sqrt[3]{11}}^{2}}{11^{1}}$

Evaluate the exponent.

$\frac{\sqrt[3]{9} {\sqrt[3]{11}}^{2}}{11}$

Step 3

Simplify the numerator.

Rewrite ${\sqrt[3]{11}}^{2}$ as ${(11^{2})}^{\frac{1}{3}}$ .

$\frac{\sqrt[3]{9} \sqrt[3]{11^{2}}}{11}$

Raise $11$ to the power of $2$ .

$\frac{\sqrt[3]{9} \sqrt[3]{121}}{11}$

Step 4

Simplify the numerator.

Combine using the product rule for radicals.

$\frac{\sqrt[3]{9 \cdot 121}}{11}$

Multiply $9$ by $121$ .

$\frac{\sqrt[3]{1089}}{11}$