# How do you simplify 12^(10/8)/12^(-3/8)?

Jun 8, 2017

See a solution process below:

#### Explanation:

Use the following rule for exponents to simplify: ${x}^{\textcolor{red}{a}} / {x}^{\textcolor{b l u e}{b}} = {x}^{\textcolor{red}{a} - \textcolor{b l u e}{b}}$

${12}^{\textcolor{red}{\frac{10}{8}}} / {12}^{\textcolor{b l u e}{- \frac{3}{8}}} = {12}^{\textcolor{red}{\frac{10}{8}} - \textcolor{b l u e}{- \frac{3}{8}}} = {12}^{\textcolor{red}{\frac{10}{8}} + \textcolor{b l u e}{\frac{3}{8}}} = {12}^{\frac{13}{8}}$

We can also rewrite this expression as:

${12}^{13 \times \frac{1}{8}}$

We can now use this rule of exponents to rewrite the expression again as:

${x}^{\textcolor{red}{a} \times \textcolor{b l u e}{b}} = {\left({x}^{\textcolor{red}{a}}\right)}^{\textcolor{b l u e}{b}}$

${12}^{\textcolor{red}{13} \times \textcolor{b l u e}{\frac{1}{8}}} = {\left({12}^{\textcolor{red}{13}}\right)}^{\textcolor{b l u e}{\frac{1}{8}}}$

If we want to simplify this to write the expression in radical form we can use this rule of exponents:

${\left({12}^{13}\right)}^{\frac{1}{\textcolor{red}{8}}} = \sqrt[\textcolor{red}{8}]{{12}^{13}}$