Precalculus Examples

${(z^{\frac{4}{3}})}^{\frac{9}{2}}$

Step 1

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

$z^{\frac{4}{3} \cdot \frac{9}{2}}$

Step 2

Cancel the common factor of $2$ .

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Step 2.1

Factor $2$ out of $4$ .

$z^{\frac{2 (2)}{3} \cdot \frac{9}{2}}$

Step 2.2

Cancel the common factor.

$z^{\frac{2 \cdot 2}{3} \cdot \frac{9}{2}}$

Step 2.3

Rewrite the expression.

$z^{\frac{2}{3} \cdot 9}$

Step 3

Cancel the common factor of $3$ .

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Step 3.1

Factor $3$ out of $9$ .

$z^{\frac{2}{3} \cdot (3 (3))}$

Step 3.2

Cancel the common factor.

$z^{\frac{2}{3} \cdot (3 \cdot 3)}$

Step 3.3

Rewrite the expression.

$z^{2 \cdot 3}$

Step 4

Multiply $2$ by $3$ .

$z^{6}$