Algebra Examples

${(27 x^{12} y^{- 21})}^{\frac{2}{3}}$

Step 1

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

${(27 x^{12} \frac{1}{y^{21}})}^{\frac{2}{3}}$

Step 2

Multiply $27 x^{12} \frac{1}{y^{21}}$ .

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Step 2.1

Combine $27$ and $\frac{1}{y^{21}}$ .

${(x^{12} \frac{27}{y^{21}})}^{\frac{2}{3}}$

Step 2.2

Combine $x^{12}$ and $\frac{27}{y^{21}}$ .

${(\frac{x^{12} \cdot 27}{y^{21}})}^{\frac{2}{3}}$

Step 3

Move $27$ to the left of $x^{12}$ .

${(\frac{27 \cdot x^{12}}{y^{21}})}^{\frac{2}{3}}$

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 $\frac{27 x^{12}}{y^{21}}$ .

$\frac{{(27 x^{12})}^{\frac{2}{3}}}{{(y^{21})}^{\frac{2}{3}}}$

Step 4.2

Apply the product rule to $27 x^{12}$ .

$\frac{27^{\frac{2}{3}} {(x^{12})}^{\frac{2}{3}}}{{(y^{21})}^{\frac{2}{3}}}$

Step 5

Simplify the numerator.

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Step 5.1

Rewrite $27$ as $3^{3}$ .

$\frac{{(3^{3})}^{\frac{2}{3}} {(x^{12})}^{\frac{2}{3}}}{{(y^{21})}^{\frac{2}{3}}}$

Step 5.2

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

$\frac{3^{3 (\frac{2}{3})} {(x^{12})}^{\frac{2}{3}}}{{(y^{21})}^{\frac{2}{3}}}$

Step 5.3

Cancel the common factor of $3$ .

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Step 5.3.1

Cancel the common factor.

$\frac{3^{3 (\frac{2}{3})} {(x^{12})}^{\frac{2}{3}}}{{(y^{21})}^{\frac{2}{3}}}$

Step 5.3.2

Rewrite the expression.

$\frac{3^{2} {(x^{12})}^{\frac{2}{3}}}{{(y^{21})}^{\frac{2}{3}}}$

Step 5.4

Raise $3$ to the power of $2$ .

$\frac{9 {(x^{12})}^{\frac{2}{3}}}{{(y^{21})}^{\frac{2}{3}}}$

Step 5.5

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

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Step 5.5.1

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

$\frac{9 x^{12 (\frac{2}{3})}}{{(y^{21})}^{\frac{2}{3}}}$

Step 5.5.2

Cancel the common factor of $3$ .

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Step 5.5.2.1

Factor $3$ out of $12$ .

$\frac{9 x^{3 (4) \frac{2}{3}}}{{(y^{21})}^{\frac{2}{3}}}$

Step 5.5.2.2

Cancel the common factor.

$\frac{9 x^{3 \cdot 4 \frac{2}{3}}}{{(y^{21})}^{\frac{2}{3}}}$

Step 5.5.2.3

Rewrite the expression.

$\frac{9 x^{4 \cdot 2}}{{(y^{21})}^{\frac{2}{3}}}$

Step 5.5.3

Multiply $4$ by $2$ .

$\frac{9 x^{8}}{{(y^{21})}^{\frac{2}{3}}}$

Step 6

Multiply the exponents in ${(y^{21})}^{\frac{2}{3}}$ .

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Step 6.1

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

$\frac{9 x^{8}}{y^{21 (\frac{2}{3})}}$

Step 6.2

Cancel the common factor of $3$ .

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Step 6.2.1

Factor $3$ out of $21$ .

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

Step 6.2.2

Cancel the common factor.

$\frac{9 x^{8}}{y^{3 \cdot 7 \frac{2}{3}}}$

Step 6.2.3

Rewrite the expression.

$\frac{9 x^{8}}{y^{7 \cdot 2}}$

Step 6.3

Multiply $7$ by $2$ .

$\frac{9 x^{8}}{y^{14}}$