Simplify the Radical Expression (4x^2)/(2x^(1/2))

$\frac{4 x^{2}}{2 x^{\frac{1}{2}}}$

Step 1

Move $x^{\frac{1}{2}}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

$\frac{4 x^{2} x^{- \frac{1}{2}}}{2}$

Step 2

Multiply $x^{2}$ by $x^{- \frac{1}{2}}$ by adding the exponents.

Move $x^{- \frac{1}{2}}$ .

$\frac{4 (x^{- \frac{1}{2}} x^{2})}{2}$

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

$\frac{4 x^{- \frac{1}{2} + 2}}{2}$

To write $2$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{4 x^{- \frac{1}{2} + 2 \cdot \frac{2}{2}}}{2}$

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

$\frac{4 x^{- \frac{1}{2} + \frac{2 \cdot 2}{2}}}{2}$

Combine the numerators over the common denominator.

$\frac{4 x^{\frac{- 1 + 2 \cdot 2}{2}}}{2}$

Simplify the numerator.

Multiply $2$ by $2$ .

$\frac{4 x^{\frac{- 1 + 4}{2}}}{2}$

Add $- 1$ and $4$ .

$\frac{4 x^{\frac{3}{2}}}{2}$

Step 3

Factor $2$ out of $4 x^{\frac{3}{2}}$ .

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

Step 4

Cancel the common factors.

Factor $2$ out of $2$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Divide $2 x^{\frac{3}{2}}$ by $1$ .

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