Simplify (a^2b^2)/( square root of c)

$\frac{a^{2} b^{2}}{\sqrt{c}}$

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

$\frac{a^{2} b^{2}}{\sqrt{c}} \cdot \frac{\sqrt{c}}{\sqrt{c}}$

Combine and simplify the denominator.

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

$\frac{a^{2} b^{2} \sqrt{c}}{\sqrt{c} \sqrt{c}}$

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

$\frac{a^{2} b^{2} \sqrt{c}}{{\sqrt{c}}^{1} \sqrt{c}}$

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

$\frac{a^{2} b^{2} \sqrt{c}}{{\sqrt{c}}^{1} {\sqrt{c}}^{1}}$

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

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

Add $1$ and $1$ .

$\frac{a^{2} b^{2} \sqrt{c}}{{\sqrt{c}}^{2}}$

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

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

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

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

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

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

$\frac{a^{2} b^{2} \sqrt{c}}{c^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{a^{2} b^{2} \sqrt{c}}{c^{\frac{2}{2}}}$

Rewrite the expression.

$\frac{a^{2} b^{2} \sqrt{c}}{c^{1}}$

Simplify.

$\frac{a^{2} b^{2} \sqrt{c}}{c}$