Algebra Examples

$2 x y^{2} {(27 y^{- 9})}^{\frac{2}{3}}$

Step 1

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

$2 x y^{2} {(27 \frac{1}{y^{9}})}^{\frac{2}{3}}$

Step 2

Combine fractions.

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Step 2.1

Combine $27$ and $\frac{1}{y^{9}}$ .

$2 x y^{2} {(\frac{27}{y^{9}})}^{\frac{2}{3}}$

Step 2.2

Apply the product rule to $\frac{27}{y^{9}}$ .

$2 x y^{2} \frac{27^{\frac{2}{3}}}{{(y^{9})}^{\frac{2}{3}}}$

Step 3

Simplify the numerator.

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Step 3.1

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

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

Step 3.2

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

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

Step 3.3

Cancel the common factor of $3$ .

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Step 3.3.1

Cancel the common factor.

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

Step 3.3.2

Rewrite the expression.

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

Step 3.4

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

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

Step 4

Simplify terms.

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Step 4.1

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

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Step 4.1.1

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

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

Step 4.1.2

Cancel the common factor of $3$ .

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Step 4.1.2.1

Factor $3$ out of $9$ .

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

Step 4.1.2.2

Cancel the common factor.

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

Step 4.1.2.3

Rewrite the expression.

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

Step 4.1.3

Multiply $3$ by $2$ .

$2 x y^{2} \frac{9}{y^{6}}$

Step 4.2

Cancel the common factor of $y^{2}$ .

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Step 4.2.1

Factor $y^{2}$ out of $2 x y^{2}$ .

$y^{2} (2 x) \frac{9}{y^{6}}$

Step 4.2.2

Factor $y^{2}$ out of $y^{6}$ .

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

Step 4.2.3

Cancel the common factor.

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

Step 4.2.4

Rewrite the expression.

$2 x \frac{9}{y^{4}}$

Step 4.3

Combine $2$ and $\frac{9}{y^{4}}$ .

$x \frac{2 \cdot 9}{y^{4}}$

Step 4.4

Multiply $2$ by $9$ .

$x \frac{18}{y^{4}}$

Step 4.5

Combine $x$ and $\frac{18}{y^{4}}$ .

$\frac{x \cdot 18}{y^{4}}$

Step 4.6

Move $18$ to the left of $x$ .

$\frac{18 x}{y^{4}}$