Algebra Examples

${(a^{- 9} b^{12} c^{18} d^{0})}^{\frac{2}{3}}$

Step 1

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

${(\frac{1}{a^{9}} b^{12} c^{18} d^{0})}^{\frac{2}{3}}$

Step 2

Combine $\frac{1}{a^{9}}$ and $b^{12}$ .

${(\frac{b^{12}}{a^{9}} c^{18} d^{0})}^{\frac{2}{3}}$

Step 3

Combine $\frac{b^{12}}{a^{9}}$ and $c^{18}$ .

${(\frac{b^{12} c^{18}}{a^{9}} d^{0})}^{\frac{2}{3}}$

Step 4

Simplify the expression.

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Step 4.1

Anything raised to $0$ is $1$ .

${(\frac{b^{12} c^{18}}{a^{9}} \cdot 1)}^{\frac{2}{3}}$

Step 4.2

Multiply $\frac{b^{12} c^{18}}{a^{9}}$ by $1$ .

${(\frac{b^{12} c^{18}}{a^{9}})}^{\frac{2}{3}}$

Step 5

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

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Step 5.1

Apply the product rule to $\frac{b^{12} c^{18}}{a^{9}}$ .

$\frac{{(b^{12} c^{18})}^{\frac{2}{3}}}{{(a^{9})}^{\frac{2}{3}}}$

Step 5.2

Apply the product rule to $b^{12} c^{18}$ .

$\frac{{(b^{12})}^{\frac{2}{3}} {(c^{18})}^{\frac{2}{3}}}{{(a^{9})}^{\frac{2}{3}}}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply the exponents in ${(b^{12})}^{\frac{2}{3}}$ .

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Step 6.1.1

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

$\frac{b^{12 (\frac{2}{3})} {(c^{18})}^{\frac{2}{3}}}{{(a^{9})}^{\frac{2}{3}}}$

Step 6.1.2

Cancel the common factor of $3$ .

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Step 6.1.2.1

Factor $3$ out of $12$ .

$\frac{b^{3 (4) \frac{2}{3}} {(c^{18})}^{\frac{2}{3}}}{{(a^{9})}^{\frac{2}{3}}}$

Step 6.1.2.2

Cancel the common factor.

$\frac{b^{3 \cdot 4 \frac{2}{3}} {(c^{18})}^{\frac{2}{3}}}{{(a^{9})}^{\frac{2}{3}}}$

Step 6.1.2.3

Rewrite the expression.

$\frac{b^{4 \cdot 2} {(c^{18})}^{\frac{2}{3}}}{{(a^{9})}^{\frac{2}{3}}}$

Step 6.1.3

Multiply $4$ by $2$ .

$\frac{b^{8} {(c^{18})}^{\frac{2}{3}}}{{(a^{9})}^{\frac{2}{3}}}$

Step 6.2

Multiply the exponents in ${(c^{18})}^{\frac{2}{3}}$ .

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Step 6.2.1

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

$\frac{b^{8} c^{18 (\frac{2}{3})}}{{(a^{9})}^{\frac{2}{3}}}$

Step 6.2.2

Cancel the common factor of $3$ .

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Step 6.2.2.1

Factor $3$ out of $18$ .

$\frac{b^{8} c^{3 (6) \frac{2}{3}}}{{(a^{9})}^{\frac{2}{3}}}$

Step 6.2.2.2

Cancel the common factor.

$\frac{b^{8} c^{3 \cdot 6 \frac{2}{3}}}{{(a^{9})}^{\frac{2}{3}}}$

Step 6.2.2.3

Rewrite the expression.

$\frac{b^{8} c^{6 \cdot 2}}{{(a^{9})}^{\frac{2}{3}}}$

Step 6.2.3

Multiply $6$ by $2$ .

$\frac{b^{8} c^{12}}{{(a^{9})}^{\frac{2}{3}}}$

Step 7

Multiply the exponents in ${(a^{9})}^{\frac{2}{3}}$ .

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Step 7.1

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

$\frac{b^{8} c^{12}}{a^{9 (\frac{2}{3})}}$

Step 7.2

Cancel the common factor of $3$ .

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Step 7.2.1

Factor $3$ out of $9$ .

$\frac{b^{8} c^{12}}{a^{3 (3) \frac{2}{3}}}$

Step 7.2.2

Cancel the common factor.

$\frac{b^{8} c^{12}}{a^{3 \cdot 3 \frac{2}{3}}}$

Step 7.2.3

Rewrite the expression.

$\frac{b^{8} c^{12}}{a^{3 \cdot 2}}$

Step 7.3

Multiply $3$ by $2$ .

$\frac{b^{8} c^{12}}{a^{6}}$