Simplify (3x)/(2 square root of x)

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

Step 1

Multiply $\frac{3 x}{2 \sqrt{x}}$ by $\frac{\sqrt{x}}{\sqrt{x}}$ .

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

Step 2

Combine and simplify the denominator.

Multiply $\frac{3 x}{2 \sqrt{x}}$ by $\frac{\sqrt{x}}{\sqrt{x}}$ .

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

Move $\sqrt{x}$ .

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

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

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

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

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

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

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

Add $1$ and $1$ .

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

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

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

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

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify.

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

Step 3

Cancel the common factor of $x$ .

Cancel the common factor.

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

Rewrite the expression.

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