# How do you write a^1.5 in radical form?

Jan 8, 2017

See full explanation below:

#### Explanation:

Because $1.5 = \frac{3}{2}$ we can rewrite this expression as:

${a}^{\frac{3}{2}}$

We can now use this rule for exponents to modify the expression:

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

${a}^{\frac{\textcolor{red}{3}}{\textcolor{b l u e}{2}}} \to {a}^{\textcolor{red}{3} \times \frac{1}{\textcolor{b l u e}{2}}} \to {\left({a}^{\textcolor{red}{3}}\right)}^{\frac{1}{\textcolor{b l u e}{2}}}$

Now we can use this rule to put this in a radical form:

${x}^{\frac{1}{\textcolor{red}{n}}} = \sqrt[\textcolor{red}{n}]{x}$

${\left({a}^{\textcolor{red}{3}}\right)}^{\frac{1}{\textcolor{b l u e}{2}}} \to \sqrt[\textcolor{b l u e}{2}]{{a}^{\textcolor{red}{3}}} \to \sqrt{{a}^{\textcolor{red}{3}}}$