Trigonometry Examples

${(8^{\frac{5}{2}})}^{\frac{2}{3}}$

Step 1

Simplify the expression.

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Step 1.1

Multiply the exponents in ${(8^{\frac{5}{2}})}^{\frac{2}{3}}$ .

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Step 1.1.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$8^{\frac{5}{2} \cdot \frac{2}{3}}$

Step 1.1.2

Cancel the common factor of $2$ .

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Step 1.1.2.1

Cancel the common factor.

$8^{\frac{5}{2} \cdot \frac{2}{3}}$

Step 1.1.2.2

Rewrite the expression.

$8^{5 (\frac{1}{3})}$

Step 1.1.3

Combine $5$ and $\frac{1}{3}$ .

$8^{\frac{5}{3}}$

Step 1.2

Rewrite $8$ as $2^{3}$ .

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

Step 1.3

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

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

Step 2

Cancel the common factor of $3$ .

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Step 2.1

Cancel the common factor.

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

Step 2.2

Rewrite the expression.

$2^{5}$

Step 3

Raise $2$ to the power of $5$ .

$32$