Algebra Examples

32^{\frac{3}{5}}

$32^{\frac{3}{5}}$

Step 1

Simplify the expression.

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Step 1.1

Rewrite

32

$32$ as

2^{5}

$2^{5}$ .

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

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

Step 1.2

Apply the power rule and multiply exponents,

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

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

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

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

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

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

Step 2

Cancel the common factor of

5

$5$ .

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Step 2.1

Cancel the common factor.

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

Step 2.2

Rewrite the expression.

$2^{3}$

$2^{3}$

Step 3

Raise

$2$ to the power of

$3$ .

$8$

$32^{\frac{3}{5}}$

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