Simplify (ab)/( square root of a)

$\frac{a b}{\sqrt{a}}$

Multiply $\frac{a b}{\sqrt{a}}$ by $\frac{\sqrt{a}}{\sqrt{a}}$ .

$\frac{a b}{\sqrt{a}} \cdot \frac{\sqrt{a}}{\sqrt{a}}$

Combine and simplify the denominator.

Multiply $\frac{a b}{\sqrt{a}}$ by $\frac{\sqrt{a}}{\sqrt{a}}$ .

$\frac{a b \sqrt{a}}{\sqrt{a} \sqrt{a}}$

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

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

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

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

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

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

Add $1$ and $1$ .

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

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

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

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

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify.

$\frac{a b \sqrt{a}}{a}$

Cancel the common factor of $a$ .

Cancel the common factor.

$\frac{a b \sqrt{a}}{a}$

Divide $b \sqrt{a}$ by $1$ .

$b \sqrt{a}$