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

1 Answer
mason m
Jan 29, 2017

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)

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