Rationalize the Denominator (x^3)/( square root of x)

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Algebra

$\frac{x^{3}}{\sqrt{x}}$

Multiply $\frac{x^{3}}{\sqrt{x}}$ by $\frac{\sqrt{x}}{\sqrt{x}}$ .

$\frac{x^{3}}{\sqrt{x}} \cdot \frac{\sqrt{x}}{\sqrt{x}}$

Combine and simplify the denominator.

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Multiply $\frac{x^{3}}{\sqrt{x}}$ and $\frac{\sqrt{x}}{\sqrt{x}}$ .

$\frac{x^{3} \sqrt{x}}{\sqrt{x} \sqrt{x}}$

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

$\frac{x^{3} \sqrt{x}}{{\sqrt{x}}^{1} \sqrt{x}}$

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

$\frac{x^{3} \sqrt{x}}{{\sqrt{x}}^{1} {\sqrt{x}}^{1}}$

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

$\frac{x^{3} \sqrt{x}}{{\sqrt{x}}^{1 + 1}}$

Add $1$ and $1$ .

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

Rewrite ${\sqrt{x}}^{2}$ as $x$ .

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

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

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

$\frac{x^{3} \sqrt{x}}{x^{\frac{1}{2} \cdot 2}}$

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

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

Cancel the common factor of $2$ .

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Cancel the common factor.

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

Rewrite the expression.

$\frac{x^{3} \sqrt{x}}{x^{1}}$

Simplify.

$\frac{x^{3} \sqrt{x}}{x}$

Cancel the common factor of $x^{3}$ and $x$ .

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Factor $x$ out of $x^{3} \sqrt{x}$ .

$\frac{x (x^{2} \sqrt{x})}{x}$

Cancel the common factors.

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Raise $x$ to the power of $1$ .

$\frac{x (x^{2} \sqrt{x})}{x^{1}}$

Factor $x$ out of $x^{1}$ .

$\frac{x (x^{2} \sqrt{x})}{x \cdot 1}$

Cancel the common factor.

$\frac{x (x^{2} \sqrt{x})}{x \cdot 1}$

Rewrite the expression.

$\frac{x^{2} \sqrt{x}}{1}$

Divide $x^{2} \sqrt{x}$ by $1$ .

$x^{2} \sqrt{x}$

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