Rationalize the Denominator (12a^2b^3)/( square root of a)

$\frac{12 a^{2} b^{3}}{\sqrt{a}}$

Multiply $\frac{12 a^{2} b^{3}}{\sqrt{a}}$ by $\frac{\sqrt{a}}{\sqrt{a}}$ .

$\frac{12 a^{2} b^{3}}{\sqrt{a}} \cdot \frac{\sqrt{a}}{\sqrt{a}}$

Combine and simplify the denominator.

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Multiply $\frac{12 a^{2} b^{3}}{\sqrt{a}}$ and $\frac{\sqrt{a}}{\sqrt{a}}$ .

$\frac{12 a^{2} b^{3} \sqrt{a}}{\sqrt{a} \sqrt{a}}$

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

$\frac{12 a^{2} b^{3} \sqrt{a}}{{\sqrt{a}}^{1} \sqrt{a}}$

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

$\frac{12 a^{2} b^{3} \sqrt{a}}{{\sqrt{a}}^{1} {\sqrt{a}}^{1}}$

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

$\frac{12 a^{2} b^{3} \sqrt{a}}{{\sqrt{a}}^{1 + 1}}$

Add $1$ and $1$ .

$\frac{12 a^{2} b^{3} \sqrt{a}}{{\sqrt{a}}^{2}}$

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

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

$\frac{12 a^{2} b^{3} \sqrt{a}}{{(a^{\frac{1}{2}})}^{2}}$

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

$\frac{12 a^{2} b^{3} \sqrt{a}}{a^{\frac{1}{2} \cdot 2}}$

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

$\frac{12 a^{2} b^{3} \sqrt{a}}{a^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

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Cancel the common factor.

$\frac{12 a^{2} b^{3} \sqrt{a}}{a^{\frac{2}{2}}}$

Divide $1$ by $1$ .

$\frac{12 a^{2} b^{3} \sqrt{a}}{a^{1}}$

Simplify.

$\frac{12 a^{2} b^{3} \sqrt{a}}{a}$

Cancel the common factor of $a^{2}$ and $a$ .

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Factor $a$ out of $12 a^{2} b^{3} \sqrt{a}$ .

$\frac{a (12 a b^{3} \sqrt{a})}{a}$

Cancel the common factors.

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

$\frac{a (12 a b^{3} \sqrt{a})}{a^{1}}$

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

$\frac{a (12 a b^{3} \sqrt{a})}{a \cdot 1}$

Cancel the common factor.

$\frac{a (12 a b^{3} \sqrt{a})}{a \cdot 1}$

Rewrite the expression.

$\frac{12 a b^{3} \sqrt{a}}{1}$

Divide $12 a b^{3} \sqrt{a}$ by $1$ .

$12 a b^{3} \sqrt{a}$

Rationalize the Denominator (12a^2b^3)/( square root of a)

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