Algebra Examples

9^{\frac{5}{2}}

$9^{\frac{5}{2}}$

Step 1

Simplify the expression.

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Step 1.1

Rewrite

$9$ as

$3^{2}$ .

${(3^{2})}^{\frac{5}{2}}$

Step 1.2

Apply the power rule and multiply exponents,

${(a^{m})}^{n} = a^{m n}$ .

$3^{2 (\frac{5}{2})}$

$3^{2 (\frac{5}{2})}$

Step 2

Cancel the common factor of

$2$ .

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Step 2.1

Cancel the common factor.

$3^{2 (\frac{5}{2})}$

Step 2.2

Rewrite the expression.

$3^{5}$

$3^{5}$

Step 3

Raise

$3$ to the power of

$5$ .

$243$

$9^{\frac{5}{2}}$

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$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$