Algebra Examples

${(\frac{- 54 x^{9}}{y^{4}})}^{\frac{2}{3}}$

Step 1

Move the negative in front of the fraction.

${(- \frac{54 x^{9}}{y^{4}})}^{\frac{2}{3}}$

Step 2

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

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Step 2.1

Apply the product rule to $- \frac{54 x^{9}}{y^{4}}$ .

${(- 1)}^{\frac{2}{3}} {(\frac{54 x^{9}}{y^{4}})}^{\frac{2}{3}}$

Step 2.2

Apply the product rule to $\frac{54 x^{9}}{y^{4}}$ .

${(- 1)}^{\frac{2}{3}} \frac{{(54 x^{9})}^{\frac{2}{3}}}{{(y^{4})}^{\frac{2}{3}}}$

Step 2.3

Apply the product rule to $54 x^{9}$ .

${(- 1)}^{\frac{2}{3}} \frac{54^{\frac{2}{3}} {(x^{9})}^{\frac{2}{3}}}{{(y^{4})}^{\frac{2}{3}}}$

Step 3

Rewrite $- 1$ as ${(- 1)}^{3}$ .

${({(- 1)}^{3})}^{\frac{2}{3}} \frac{54^{\frac{2}{3}} {(x^{9})}^{\frac{2}{3}}}{{(y^{4})}^{\frac{2}{3}}}$

Step 4

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

${(- 1)}^{3 (\frac{2}{3})} \frac{54^{\frac{2}{3}} {(x^{9})}^{\frac{2}{3}}}{{(y^{4})}^{\frac{2}{3}}}$

Step 5

Cancel the common factor of $3$ .

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Step 5.1

Cancel the common factor.

${(- 1)}^{3 (\frac{2}{3})} \frac{54^{\frac{2}{3}} {(x^{9})}^{\frac{2}{3}}}{{(y^{4})}^{\frac{2}{3}}}$

Step 5.2

Rewrite the expression.

${(- 1)}^{2} \frac{54^{\frac{2}{3}} {(x^{9})}^{\frac{2}{3}}}{{(y^{4})}^{\frac{2}{3}}}$

Step 6

Raise $- 1$ to the power of $2$ .

$1 \frac{54^{\frac{2}{3}} {(x^{9})}^{\frac{2}{3}}}{{(y^{4})}^{\frac{2}{3}}}$

Step 7

Multiply $\frac{54^{\frac{2}{3}} {(x^{9})}^{\frac{2}{3}}}{{(y^{4})}^{\frac{2}{3}}}$ by $1$ .

$\frac{54^{\frac{2}{3}} {(x^{9})}^{\frac{2}{3}}}{{(y^{4})}^{\frac{2}{3}}}$

Step 8

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

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Step 8.1

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

$\frac{54^{\frac{2}{3}} x^{9 (\frac{2}{3})}}{{(y^{4})}^{\frac{2}{3}}}$

Step 8.2

Cancel the common factor of $3$ .

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Step 8.2.1

Factor $3$ out of $9$ .

$\frac{54^{\frac{2}{3}} x^{3 (3) \frac{2}{3}}}{{(y^{4})}^{\frac{2}{3}}}$

Step 8.2.2

Cancel the common factor.

$\frac{54^{\frac{2}{3}} x^{3 \cdot 3 \frac{2}{3}}}{{(y^{4})}^{\frac{2}{3}}}$

Step 8.2.3

Rewrite the expression.

$\frac{54^{\frac{2}{3}} x^{3 \cdot 2}}{{(y^{4})}^{\frac{2}{3}}}$

Step 8.3

Multiply $3$ by $2$ .

$\frac{54^{\frac{2}{3}} x^{6}}{{(y^{4})}^{\frac{2}{3}}}$

Step 9

Multiply the exponents in ${(y^{4})}^{\frac{2}{3}}$ .

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Step 9.1

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

$\frac{54^{\frac{2}{3}} x^{6}}{y^{4 (\frac{2}{3})}}$

Step 9.2

Multiply $4 (\frac{2}{3})$ .

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Step 9.2.1

Combine $4$ and $\frac{2}{3}$ .

$\frac{54^{\frac{2}{3}} x^{6}}{y^{\frac{4 \cdot 2}{3}}}$

Step 9.2.2

Multiply $4$ by $2$ .

$\frac{54^{\frac{2}{3}} x^{6}}{y^{\frac{8}{3}}}$

Step 10

Reorder factors in $\frac{54^{\frac{2}{3}} x^{6}}{y^{\frac{8}{3}}}$ .

$\frac{x^{6} \cdot 54^{\frac{2}{3}}}{y^{\frac{8}{3}}}$