Algebra Examples

${(8 w^{7} x^{- 5} y^{3} z^{- 9})}^{- \frac{2}{3}}$

Step 1

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

${(8 w^{7} \frac{1}{x^{5}} y^{3} z^{- 9})}^{- \frac{2}{3}}$

Step 2

Multiply $8 w^{7} \frac{1}{x^{5}}$ .

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Step 2.1

Combine $8$ and $\frac{1}{x^{5}}$ .

${(w^{7} \frac{8}{x^{5}} y^{3} z^{- 9})}^{- \frac{2}{3}}$

Step 2.2

Combine $w^{7}$ and $\frac{8}{x^{5}}$ .

${(\frac{w^{7} \cdot 8}{x^{5}} y^{3} z^{- 9})}^{- \frac{2}{3}}$

Step 3

Move $8$ to the left of $w^{7}$ .

${(\frac{8 \cdot w^{7}}{x^{5}} y^{3} z^{- 9})}^{- \frac{2}{3}}$

Step 4

Combine $\frac{8 w^{7}}{x^{5}}$ and $y^{3}$ .

${(\frac{8 w^{7} y^{3}}{x^{5}} z^{- 9})}^{- \frac{2}{3}}$

Step 5

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

${(\frac{8 w^{7} y^{3}}{x^{5}} \cdot \frac{1}{z^{9}})}^{- \frac{2}{3}}$

Step 6

Combine.

${(\frac{8 w^{7} y^{3} \cdot 1}{x^{5} z^{9}})}^{- \frac{2}{3}}$

Step 7

Multiply $8$ by $1$ .

${(\frac{8 w^{7} y^{3}}{x^{5} z^{9}})}^{- \frac{2}{3}}$

Step 8

Change the sign of the exponent by rewriting the base as its reciprocal.

${(\frac{x^{5} z^{9}}{8 w^{7} y^{3}})}^{\frac{2}{3}}$

Step 9

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

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Step 9.1

Apply the product rule to $\frac{x^{5} z^{9}}{8 w^{7} y^{3}}$ .

$\frac{{(x^{5} z^{9})}^{\frac{2}{3}}}{{(8 w^{7} y^{3})}^{\frac{2}{3}}}$

Step 9.2

Apply the product rule to $x^{5} z^{9}$ .

$\frac{{(x^{5})}^{\frac{2}{3}} {(z^{9})}^{\frac{2}{3}}}{{(8 w^{7} y^{3})}^{\frac{2}{3}}}$

Step 9.3

Apply the product rule to $8 w^{7} y^{3}$ .

$\frac{{(x^{5})}^{\frac{2}{3}} {(z^{9})}^{\frac{2}{3}}}{{(8 w^{7})}^{\frac{2}{3}} {(y^{3})}^{\frac{2}{3}}}$

Step 9.4

Apply the product rule to $8 w^{7}$ .

$\frac{{(x^{5})}^{\frac{2}{3}} {(z^{9})}^{\frac{2}{3}}}{8^{\frac{2}{3}} {(w^{7})}^{\frac{2}{3}} {(y^{3})}^{\frac{2}{3}}}$

Step 10

Simplify the numerator.

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Step 10.1

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

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Step 10.1.1

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

$\frac{x^{5 (\frac{2}{3})} {(z^{9})}^{\frac{2}{3}}}{8^{\frac{2}{3}} {(w^{7})}^{\frac{2}{3}} {(y^{3})}^{\frac{2}{3}}}$

Step 10.1.2

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

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Step 10.1.2.1

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

$\frac{x^{\frac{5 \cdot 2}{3}} {(z^{9})}^{\frac{2}{3}}}{8^{\frac{2}{3}} {(w^{7})}^{\frac{2}{3}} {(y^{3})}^{\frac{2}{3}}}$

Step 10.1.2.2

Multiply $5$ by $2$ .

$\frac{x^{\frac{10}{3}} {(z^{9})}^{\frac{2}{3}}}{8^{\frac{2}{3}} {(w^{7})}^{\frac{2}{3}} {(y^{3})}^{\frac{2}{3}}}$

Step 10.2

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

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Step 10.2.1

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

$\frac{x^{\frac{10}{3}} z^{9 (\frac{2}{3})}}{8^{\frac{2}{3}} {(w^{7})}^{\frac{2}{3}} {(y^{3})}^{\frac{2}{3}}}$

Step 10.2.2

Cancel the common factor of $3$ .

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Step 10.2.2.1

Factor $3$ out of $9$ .

$\frac{x^{\frac{10}{3}} z^{3 (3) \frac{2}{3}}}{8^{\frac{2}{3}} {(w^{7})}^{\frac{2}{3}} {(y^{3})}^{\frac{2}{3}}}$

Step 10.2.2.2

Cancel the common factor.

$\frac{x^{\frac{10}{3}} z^{3 \cdot 3 \frac{2}{3}}}{8^{\frac{2}{3}} {(w^{7})}^{\frac{2}{3}} {(y^{3})}^{\frac{2}{3}}}$

Step 10.2.2.3

Rewrite the expression.

$\frac{x^{\frac{10}{3}} z^{3 \cdot 2}}{8^{\frac{2}{3}} {(w^{7})}^{\frac{2}{3}} {(y^{3})}^{\frac{2}{3}}}$

Step 10.2.3

Multiply $3$ by $2$ .

$\frac{x^{\frac{10}{3}} z^{6}}{8^{\frac{2}{3}} {(w^{7})}^{\frac{2}{3}} {(y^{3})}^{\frac{2}{3}}}$

Step 11

Simplify the denominator.

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Step 11.1

Rewrite $8$ as $2^{3}$ .

$\frac{x^{\frac{10}{3}} z^{6}}{{(2^{3})}^{\frac{2}{3}} {(w^{7})}^{\frac{2}{3}} {(y^{3})}^{\frac{2}{3}}}$

Step 11.2

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

$\frac{x^{\frac{10}{3}} z^{6}}{2^{3 (\frac{2}{3})} {(w^{7})}^{\frac{2}{3}} {(y^{3})}^{\frac{2}{3}}}$

Step 11.3

Cancel the common factor of $3$ .

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Step 11.3.1

Cancel the common factor.

$\frac{x^{\frac{10}{3}} z^{6}}{2^{3 (\frac{2}{3})} {(w^{7})}^{\frac{2}{3}} {(y^{3})}^{\frac{2}{3}}}$

Step 11.3.2

Rewrite the expression.

$\frac{x^{\frac{10}{3}} z^{6}}{2^{2} {(w^{7})}^{\frac{2}{3}} {(y^{3})}^{\frac{2}{3}}}$

Step 11.4

Raise $2$ to the power of $2$ .

$\frac{x^{\frac{10}{3}} z^{6}}{4 {(w^{7})}^{\frac{2}{3}} {(y^{3})}^{\frac{2}{3}}}$

Step 11.5

Multiply the exponents in ${(w^{7})}^{\frac{2}{3}}$ .

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Step 11.5.1

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

$\frac{x^{\frac{10}{3}} z^{6}}{4 w^{7 (\frac{2}{3})} {(y^{3})}^{\frac{2}{3}}}$

Step 11.5.2

Multiply $7 (\frac{2}{3})$ .

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Step 11.5.2.1

Combine $7$ and $\frac{2}{3}$ .

$\frac{x^{\frac{10}{3}} z^{6}}{4 w^{\frac{7 \cdot 2}{3}} {(y^{3})}^{\frac{2}{3}}}$

Step 11.5.2.2

Multiply $7$ by $2$ .

$\frac{x^{\frac{10}{3}} z^{6}}{4 w^{\frac{14}{3}} {(y^{3})}^{\frac{2}{3}}}$

Step 11.6

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

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Step 11.6.1

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

$\frac{x^{\frac{10}{3}} z^{6}}{4 w^{\frac{14}{3}} y^{3 (\frac{2}{3})}}$

Step 11.6.2

Cancel the common factor of $3$ .

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Step 11.6.2.1

Cancel the common factor.

$\frac{x^{\frac{10}{3}} z^{6}}{4 w^{\frac{14}{3}} y^{3 (\frac{2}{3})}}$

Step 11.6.2.2

Rewrite the expression.

$\frac{x^{\frac{10}{3}} z^{6}}{4 w^{\frac{14}{3}} y^{2}}$

Step 12

Reorder factors in $\frac{x^{\frac{10}{3}} z^{6}}{4 w^{\frac{14}{3}} y^{2}}$ .

$\frac{z^{6} x^{\frac{10}{3}}}{4 y^{2} w^{\frac{14}{3}}}$