# How do you simplify 9^(3/2)?

May 25, 2016

$27$

#### Explanation:

Breaking ${9}^{\frac{3}{2}}$ down into its component parts

$\frac{3}{2}$ is the same as $3 \times \frac{1}{2}$ which is the same as $\frac{1}{2} \times 3$

so ${9}^{\frac{3}{2}}$ is the same as ${9}^{\frac{1}{2} \times 3}$

Write this as: ${\left({9}^{\frac{1}{2}}\right)}^{3}$

Consider the part of ${9}^{\frac{1}{2}}$

This is the same as $\sqrt{9} = 3$

So ${\left({9}^{\frac{1}{2}}\right)}^{3} = {\left(\sqrt{9}\right)}^{3}$

$= {3}^{3} = 27$
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However, it true to say that:

$\sqrt{9} = \pm 3$

and ${\left(\pm 3\right)}^{3} = \pm 27$