# How do you multiply (3sqrtx^5)(2sqrtx^3)?

Mar 3, 2018

The answer is $6 {x}^{4}$.

#### Explanation:

You can rewrite ${\sqrt{x}}^{5}$ as ${x}^{\frac{5}{2}}$, and ${\sqrt{x}}^{3}$ as ${x}^{\frac{3}{2}}$:

$\textcolor{w h i t e}{=} \left(3 {\sqrt{x}}^{5}\right) \left(2 {\sqrt{x}}^{3}\right)$

$= \left(3 {x}^{\frac{5}{2}}\right) \left(2 {x}^{\frac{3}{2}}\right)$

$= 3 \cdot 2 \cdot {x}^{\frac{5}{2}} \cdot {x}^{\frac{3}{2}}$

$= 6 \cdot {x}^{\frac{5}{2}} \cdot {x}^{\frac{3}{2}}$

$= 6 \cdot {x}^{\frac{5}{2} + \frac{3}{2}}$

$= 6 \cdot {x}^{\frac{8}{2}}$

$= 6 \cdot {x}^{4}$

The answer is $6 {x}^{4}$.