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

1 Answer
Jan 27, 2016

Answer:

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

Explanation:

First things first we write:

#2sqrt(x)=2x^(1/2)#
#5sqrt(x^3)=5x^(3/2)#

The constant terms can be multiplied directly giving

#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*x^b=x^(a+b)#

So our final answer is

#2x^(1/2)*5x^(3/2)=10x^(1/2)x^(3/2)=10x^2#