Basic Math Examples

${(a^{- 5} b^{2} c^{15})}^{\frac{3}{5}}$

Step 1

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

${(\frac{1}{a^{5}} b^{2} c^{15})}^{\frac{3}{5}}$

Step 2

Combine $\frac{1}{a^{5}}$ and $b^{2}$ .

${(\frac{b^{2}}{a^{5}} c^{15})}^{\frac{3}{5}}$

Step 3

Combine $\frac{b^{2}}{a^{5}}$ and $c^{15}$ .

${(\frac{b^{2} c^{15}}{a^{5}})}^{\frac{3}{5}}$

Step 4

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 4.1

Apply the product rule to $\frac{b^{2} c^{15}}{a^{5}}$ .

$\frac{{(b^{2} c^{15})}^{\frac{3}{5}}}{{(a^{5})}^{\frac{3}{5}}}$

Step 4.2

Apply the product rule to $b^{2} c^{15}$ .

$\frac{{(b^{2})}^{\frac{3}{5}} {(c^{15})}^{\frac{3}{5}}}{{(a^{5})}^{\frac{3}{5}}}$

Step 5

Simplify the numerator.

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Step 5.1

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

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Step 5.1.1

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

$\frac{b^{2 (\frac{3}{5})} {(c^{15})}^{\frac{3}{5}}}{{(a^{5})}^{\frac{3}{5}}}$

Step 5.1.2

Multiply $2 (\frac{3}{5})$ .

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Step 5.1.2.1

Combine $2$ and $\frac{3}{5}$ .

$\frac{b^{\frac{2 \cdot 3}{5}} {(c^{15})}^{\frac{3}{5}}}{{(a^{5})}^{\frac{3}{5}}}$

Step 5.1.2.2

Multiply $2$ by $3$ .

$\frac{b^{\frac{6}{5}} {(c^{15})}^{\frac{3}{5}}}{{(a^{5})}^{\frac{3}{5}}}$

Step 5.2

Multiply the exponents in ${(c^{15})}^{\frac{3}{5}}$ .

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Step 5.2.1

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

$\frac{b^{\frac{6}{5}} c^{15 (\frac{3}{5})}}{{(a^{5})}^{\frac{3}{5}}}$

Step 5.2.2

Cancel the common factor of $5$ .

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Step 5.2.2.1

Factor $5$ out of $15$ .

$\frac{b^{\frac{6}{5}} c^{5 (3) \frac{3}{5}}}{{(a^{5})}^{\frac{3}{5}}}$

Step 5.2.2.2

Cancel the common factor.

$\frac{b^{\frac{6}{5}} c^{5 \cdot 3 \frac{3}{5}}}{{(a^{5})}^{\frac{3}{5}}}$

Step 5.2.2.3

Rewrite the expression.

$\frac{b^{\frac{6}{5}} c^{3 \cdot 3}}{{(a^{5})}^{\frac{3}{5}}}$

Step 5.2.3

Multiply $3$ by $3$ .

$\frac{b^{\frac{6}{5}} c^{9}}{{(a^{5})}^{\frac{3}{5}}}$

Step 6

Simplify the expression.

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Step 6.1

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

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Step 6.1.1

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

$\frac{b^{\frac{6}{5}} c^{9}}{a^{5 (\frac{3}{5})}}$

Step 6.1.2

Cancel the common factor of $5$ .

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Step 6.1.2.1

Cancel the common factor.

$\frac{b^{\frac{6}{5}} c^{9}}{a^{5 (\frac{3}{5})}}$

Step 6.1.2.2

Rewrite the expression.

$\frac{b^{\frac{6}{5}} c^{9}}{a^{3}}$

Step 6.2

Reorder factors in $\frac{b^{\frac{6}{5}} c^{9}}{a^{3}}$ .

$\frac{c^{9} b^{\frac{6}{5}}}{a^{3}}$