How do you multiply # ( 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:

#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#