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

Jan 29, 2017

${x}^{2} \cdot {x}^{\sqrt{3}} = {x}^{2 + \sqrt{3}}$

#### Explanation:

Imagine, first, we wanted to simplify the expression ${x}^{2} \cdot {x}^{3}$. Recall that a power of $2$ simply means "multiplied by itself twice."

Then,

${x}^{2} \cdot {x}^{3} = {\overbrace{x \cdot x}}^{{x}^{2}} \cdot {\overbrace{x \cdot x \cdot x}}^{{x}^{3}} = {\overbrace{x \cdot x \cdot x \cdot x \cdot x}}^{{x}^{5}} = {x}^{5}$

In general, we can write that:

${x}^{a} \cdot {x}^{b} = {\overbrace{x \cdot x \cdot \ldots \cdot x}}^{\text{x multiplied a times")*overbrace(x*x*...*x)^("x multiplied b times")=overbrace(x*x*...*x)^("x multiplied a+b times}} = {x}^{a + b}$

In the given problem, one of the powers is $\sqrt{3}$, an irrational number. However, this has no bearing on the above rule ${x}^{a} \cdot {x}^{b} = {x}^{a + b}$.

${x}^{2} \cdot {x}^{\sqrt{3}} = {x}^{2 + \sqrt{3}}$