Pre-Algebra Examples

${(b^{\frac{1}{3}} \cdot c^{- 2})}^{\frac{2}{5}}$

Step 1

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

${(b^{\frac{1}{3}} \cdot \frac{1}{c^{2}})}^{\frac{2}{5}}$

Step 2

Combine $b^{\frac{1}{3}}$ and $\frac{1}{c^{2}}$ .

${(\frac{b^{\frac{1}{3}}}{c^{2}})}^{\frac{2}{5}}$

Step 3

Apply basic rules of exponents.

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Step 3.1

Apply the product rule to $\frac{b^{\frac{1}{3}}}{c^{2}}$ .

$\frac{{(b^{\frac{1}{3}})}^{\frac{2}{5}}}{{(c^{2})}^{\frac{2}{5}}}$

Step 3.2

Multiply the exponents in ${(b^{\frac{1}{3}})}^{\frac{2}{5}}$ .

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Step 3.2.1

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

$\frac{b^{\frac{1}{3} \cdot \frac{2}{5}}}{{(c^{2})}^{\frac{2}{5}}}$

Step 3.2.2

Multiply $\frac{1}{3} \cdot \frac{2}{5}$ .

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Step 3.2.2.1

Multiply $\frac{1}{3}$ by $\frac{2}{5}$ .

$\frac{b^{\frac{2}{3 \cdot 5}}}{{(c^{2})}^{\frac{2}{5}}}$

Step 3.2.2.2

Multiply $3$ by $5$ .

$\frac{b^{\frac{2}{15}}}{{(c^{2})}^{\frac{2}{5}}}$

Step 3.3

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

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Step 3.3.1

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

$\frac{b^{\frac{2}{15}}}{c^{2 (\frac{2}{5})}}$

Step 3.3.2

Multiply $2 (\frac{2}{5})$ .

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Step 3.3.2.1

Combine $2$ and $\frac{2}{5}$ .

$\frac{b^{\frac{2}{15}}}{c^{\frac{2 \cdot 2}{5}}}$

Step 3.3.2.2

Multiply $2$ by $2$ .

$\frac{b^{\frac{2}{15}}}{c^{\frac{4}{5}}}$