# How do you write 10 to the 1.5th power?

Nov 4, 2015

${10}^{1.5} = \pm 10 \sqrt{10}$

#### Explanation:

${10}^{1.5} = {10}^{\frac{3}{2}}$

$\textcolor{w h i t e}{\text{XX}} = {\left({10}^{\frac{1}{2}}\right)}^{3}$

$\textcolor{w h i t e}{\text{XX}} = {\left(\pm \sqrt{10}\right)}^{3}$

$\textcolor{w h i t e}{\text{XX}} = {\left(\pm \sqrt{10}\right)}^{2} \times {\left(\pm \sqrt{10}\right)}^{1}$

$\textcolor{w h i t e}{\text{XX}} = 10 \times \left(\pm \sqrt{10}\right)$

$\textcolor{w h i t e}{\text{XX}} = \pm 10 \sqrt{10}$

Sorry if I've overdone the details; also depending upon your instructor, only the primary root ($10 \sqrt{10}$) might be expected as an answer.