Simplify 4x^2*x^(1/2)

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

Step 1

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

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

Step 2

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

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

Step 3

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

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

Step 4

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

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

Step 5

Combine the numerators over the common denominator.

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

Step 6

Simplify the numerator.

Multiply $2$ by $2$ .

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

Add $1$ and $4$ .

$4 x^{\frac{5}{2}}$