Rationalize the Denominator (4x^3)/( square root of 7x+11)

$\frac{4 x^{3}}{\sqrt{7 x + 11}}$

Multiply $\frac{4 x^{3}}{\sqrt{7 x + 11}}$ by $\frac{\sqrt{7 x + 11}}{\sqrt{7 x + 11}}$ .

$\frac{4 x^{3}}{\sqrt{7 x + 11}} \cdot \frac{\sqrt{7 x + 11}}{\sqrt{7 x + 11}}$

Combine and simplify the denominator.

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Multiply $\frac{4 x^{3}}{\sqrt{7 x + 11}}$ and $\frac{\sqrt{7 x + 11}}{\sqrt{7 x + 11}}$ .

$\frac{4 x^{3} \sqrt{7 x + 11}}{\sqrt{7 x + 11} \sqrt{7 x + 11}}$

Raise $\sqrt{7 x + 11}$ to the power of $1$ .

$\frac{4 x^{3} \sqrt{7 x + 11}}{{\sqrt{7 x + 11}}^{1} \sqrt{7 x + 11}}$

Raise $\sqrt{7 x + 11}$ to the power of $1$ .

$\frac{4 x^{3} \sqrt{7 x + 11}}{{\sqrt{7 x + 11}}^{1} {\sqrt{7 x + 11}}^{1}}$

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

$\frac{4 x^{3} \sqrt{7 x + 11}}{{\sqrt{7 x + 11}}^{1 + 1}}$

Add $1$ and $1$ .

$\frac{4 x^{3} \sqrt{7 x + 11}}{{\sqrt{7 x + 11}}^{2}}$

Rewrite ${\sqrt{7 x + 11}}^{2}$ as $7 x + 11$ .

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Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{7 x + 11}$ as ${(7 x + 11)}^{\frac{1}{2}}$ .

$\frac{4 x^{3} \sqrt{7 x + 11}}{{({(7 x + 11)}^{\frac{1}{2}})}^{2}}$

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

$\frac{4 x^{3} \sqrt{7 x + 11}}{{(7 x + 11)}^{\frac{1}{2} \cdot 2}}$

Combine $\frac{1}{2}$ and $2$ .

$\frac{4 x^{3} \sqrt{7 x + 11}}{{(7 x + 11)}^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

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Cancel the common factor.

$\frac{4 x^{3} \sqrt{7 x + 11}}{{(7 x + 11)}^{\frac{2}{2}}}$

Divide $1$ by $1$ .

$\frac{4 x^{3} \sqrt{7 x + 11}}{{(7 x + 11)}^{1}}$

Simplify.

$\frac{4 x^{3} \sqrt{7 x + 11}}{7 x + 11}$

Rationalize the Denominator (4x^3)/( square root of 7x+11)

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