How do you multiply $(2 \sqrt{x}) (5 {\sqrt{x}}^{3})$ $( 2 sqrt x) ( 5 sqrt x ^3 )$ ?

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Answer 1 · 2016-01-27T22:29:33

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

First things first we write:

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

The constant terms can be multiplied directly giving

$2 x^{\frac{1}{2}} \cdot 5 x^{\frac{3}{2}} = 10 x^{\frac{1}{2}} x^{\frac{3}{2}}$ $2x^(1/2)*5x^(3/2)=10x^(1/2)x^(3/2)$

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

$x^{a} \cdot x^{b} = x^{a + b}$ $x^a*x^b=x^(a+b)$

So our final answer is

$2 x^{\frac{1}{2}} \cdot 5 x^{\frac{3}{2}} = 10 x^{\frac{1}{2}} x^{\frac{3}{2}} = 10 x^{2}$ $2x^(1/2)*5x^(3/2)=10x^(1/2)x^(3/2)=10x^2$

How do you multiply (2√x)(5√x3) ( 2 sqrt x) ( 5 sqrt x ^3 )?