How do you simplify 9^{\frac{3}{2}}?

Sallie Banks 2022-01-03 Answered
How do you simplify \(\displaystyle{9}^{{{\frac{{{3}}}{{{2}}}}}}\)?

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Expert Answer

Joseph Lewis
Answered 2022-01-04 Author has 4556 answers

Explanation:
Breaking \(\displaystyle{9}^{{{\frac{{{3}}}{{{2}}}}}}\) down into its component parts
\(\displaystyle{\frac{{{3}}}{{{2}}}}\) is the same as \(\displaystyle{3}\times{\frac{{{1}}}{{{2}}}}\) which is the same as \(\displaystyle{\frac{{{1}}}{{{2}}}}\times{3}\)
so \(\displaystyle{9}^{{{\frac{{{3}}}{{{2}}}}}}\) is the same as \(9^{\frac{1}{2}\times3}\)
Write this as: \(\displaystyle{\left({9}^{{{\frac{{{1}}}{{{2}}}}}}\right)}^{{3}}\)
Consider the part of \(\displaystyle{9}^{{{\frac{{{1}}}{{{2}}}}}}\)
This is the same as \(\displaystyle\sqrt{{{9}}}={3}\)
So \(\displaystyle{\left({9}^{{{\frac{{{1}}}{{{2}}}}}}\right)}^{{3}}={\left(\sqrt{{{9}}}\right)}^{{3}}\)
\(\displaystyle{3}^{{3}}={27}\)
However, it true to say that:
\(\displaystyle\sqrt{{{9}}}=\pm{3}\)
and \(\displaystyle{\left(\pm{3}\right)}^{{3}}=\pm{27}\)

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Timothy Wolff
Answered 2022-01-05 Author has 1852 answers
Simplify the expression.
\(\displaystyle{3}^{{{2}{\left({\frac{{{3}}}{{{2}}}}\right)}}}\)
Cancel the common factor of 2
\(\displaystyle{3}^{{3}}\)
Raise 3 to the power of 3 .
27
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Vasquez
Answered 2022-01-09 Author has 8850 answers

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

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