Finite Math Examples

${(y^{3} \cdot z^{- \frac{1}{3}})}^{\frac{4}{3}}$

Step 1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

${(y^{3} \cdot \frac{1}{z^{\frac{1}{3}}})}^{\frac{4}{3}}$

Step 2

Combine $y^{3}$ and $\frac{1}{z^{\frac{1}{3}}}$ .

${(\frac{y^{3}}{z^{\frac{1}{3}}})}^{\frac{4}{3}}$

Step 3

Apply basic rules of exponents.

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Step 3.1

Apply the product rule to $\frac{y^{3}}{z^{\frac{1}{3}}}$ .

$\frac{{(y^{3})}^{\frac{4}{3}}}{{(z^{\frac{1}{3}})}^{\frac{4}{3}}}$

Step 3.2

Multiply the exponents in ${(y^{3})}^{\frac{4}{3}}$ .

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Step 3.2.1

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

$\frac{y^{3 (\frac{4}{3})}}{{(z^{\frac{1}{3}})}^{\frac{4}{3}}}$

Step 3.2.2

Cancel the common factor of $3$ .

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Step 3.2.2.1

Cancel the common factor.

$\frac{y^{3 (\frac{4}{3})}}{{(z^{\frac{1}{3}})}^{\frac{4}{3}}}$

Step 3.2.2.2

Rewrite the expression.

$\frac{y^{4}}{{(z^{\frac{1}{3}})}^{\frac{4}{3}}}$

Step 3.3

Multiply the exponents in ${(z^{\frac{1}{3}})}^{\frac{4}{3}}$ .

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Step 3.3.1

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

$\frac{y^{4}}{z^{\frac{1}{3} \cdot \frac{4}{3}}}$

Step 3.3.2

Multiply $\frac{1}{3} \cdot \frac{4}{3}$ .

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Step 3.3.2.1

Multiply $\frac{1}{3}$ by $\frac{4}{3}$ .

$\frac{y^{4}}{z^{\frac{4}{3 \cdot 3}}}$

Step 3.3.2.2

Multiply $3$ by $3$ .

$\frac{y^{4}}{z^{\frac{4}{9}}}$