# How do you simplify p^(1/3)timesp^(1/2)?

Jan 3, 2017

See full simplification process below:

#### Explanation:

The first step is to get each exponent over the same common denominator (in this case $\textcolor{red}{6}$ by multiplying by a form of $\textcolor{b l u e}{1}$ so we can then use the rules for exponents to simplify this expression:

${p}^{\textcolor{red}{\frac{1}{3}}} \times {p}^{\textcolor{p u r p \le}{\frac{1}{2}}} = {p}^{\textcolor{red}{\frac{1}{3} \times \frac{2}{2}}} \times {p}^{\textcolor{p u r p \le}{\frac{1}{2} \times \frac{3}{3}}} = {p}^{\textcolor{red}{\frac{2}{6}}} \times {p}^{\textcolor{p u r p \le}{\frac{3}{6}}}$

We can now use the following rule for exponents to combine the terms of this expression:

${a}^{\textcolor{red}{a}} \times {x}^{\textcolor{p u r p \le}{b}} = {x}^{\textcolor{red}{a} + \textcolor{p u r p \le}{b}}$

Giving

${p}^{\textcolor{red}{\frac{2}{6}}} \times {p}^{\textcolor{p u r p \le}{\frac{3}{6}}} = {p}^{\textcolor{red}{\frac{2}{6}} + \textcolor{p u r p \le}{\frac{3}{6}}} = {p}^{\frac{5}{6}}$