How do you simplify #x^2*x^sqrt3#?

1 Answer
Jan 29, 2017

Answer:

#x^2*x^sqrt3=x^(2+sqrt3)#

Explanation:

Imagine, first, we wanted to simplify the expression #x^2*x^3#. Recall that a power of #2# simply means "multiplied by itself twice."

Then,

#x^2*x^3=overbrace(x*x)^(x^2)*overbrace(x*x*x)^(x^3)=overbrace(x*x*x*x*x)^(x^5)=x^5#

In general, we can write that:

#x^a*x^b=overbrace(x*x*...*x)^("x multiplied a times")*overbrace(x*x*...*x)^("x multiplied b times")=overbrace(x*x*...*x)^("x multiplied a+b times")=x^(a+b)#

In the given problem, one of the powers is #sqrt3#, an irrational number. However, this has no bearing on the above rule #x^a*x^b=x^(a+b)#.

#x^2*x^sqrt3=x^(2+sqrt3)#