How do you simplify $9^{\frac{3}{2}}$ $9^(3/2)$ ?

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Answer 1 · 2016-05-25T09:18:39

$27$ $27$

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

$\frac{3}{2}$ $3/2$ is the same as $3 \times \frac{1}{2}$ $3xx1/2$ which is the same as $\frac{1}{2} \times 3$ $1/2xx3$

so $9^{\frac{3}{2}}$ $9^(3/2)$ is the same as $9^{\frac{1}{2} \times 3}$ $9^(1/2xx3)$

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

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

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

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

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

$\sqrt{9} = \pm 3$ $sqrt(9)=+-3$

and ${(\pm 3)}^{3} = \pm 27$ $(+-3)^3=+-27$

How do you simplify 9^(3/2)9329^(3/2)?