Expert Answer to "How do you simplify 932?"

Sallie Banks

Answered question

2022-01-03

How do you simplify

9^{\frac{3}{2}}

Answer & Explanation

Joseph Lewis

Beginner2022-01-04Added 43 answers

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: ${(9^{\frac{1}{2}})}^{3}$
Consider the part of $9^{\frac{1}{2}}$
This is the same as $\sqrt{9} = 3$
So ${(9^{\frac{1}{2}})}^{3} = {(\sqrt{9})}^{3}$
$3^{3} = 27$
However, it true to say that:
$\sqrt{9} = \pm 3$
and ${(\pm 3)}^{3} = \pm 27$

Timothy Wolff

Beginner2022-01-05Added 26 answers

Simplify the expression.

3^{2 (\frac{3}{2})}

Cancel the common factor of 2

3^{3}

Raise 3 to the power of 3 .
27

Vasquez

Expert2022-01-09Added 669 answers

$\begin{matrix} \Rightarrow (9)^{\frac{3}{2}} \\ \Rightarrow (3^{2})^{\frac{3}{2}} \\ \Rightarrow 3^{2 \cdot \frac{3}{2}} \\ \Rightarrow 3^{3} = 27 \end{matrix}$

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