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

Jan 27, 2016

Convert to fractional exponents, and then use the law of exponents concerning multiplication.

#### Explanation:

First things first we write:

$2 \sqrt{x} = 2 {x}^{\frac{1}{2}}$
$5 \sqrt{{x}^{3}} = 5 {x}^{\frac{3}{2}}$

The constant terms can be multiplied directly giving

$2 {x}^{\frac{1}{2}} \cdot 5 {x}^{\frac{3}{2}} = 10 {x}^{\frac{1}{2}} {x}^{\frac{3}{2}}$

Then the laws of exponents tell us that two of the same base are multiplied, there exponents are summed, or:

${x}^{a} \cdot {x}^{b} = {x}^{a + b}$

$2 {x}^{\frac{1}{2}} \cdot 5 {x}^{\frac{3}{2}} = 10 {x}^{\frac{1}{2}} {x}^{\frac{3}{2}} = 10 {x}^{2}$