Algebra Examples

${(x^{- 2} y^{- 3})}^{2} \cdot 2 x y^{2}$

Step 1

Rewrite using the commutative property of multiplication.

$2 {(x^{- 2} y^{- 3})}^{2} x y^{2}$

Step 2

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

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

Step 3

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

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

Step 4

Combine.

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

Step 5

Multiply $1$ by $1$ .

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

Step 6

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

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Step 6.1

Apply the product rule to $\frac{1}{x^{2} y^{3}}$ .

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

Step 6.2

Apply the product rule to $x^{2} y^{3}$ .

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

Step 7

One to any power is one.

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

Step 8

Simplify the denominator.

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Step 8.1

Multiply the exponents in ${(x^{2})}^{2}$ .

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Step 8.1.1

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

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

Step 8.1.2

Multiply $2$ by $2$ .

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

Step 8.2

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

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Step 8.2.1

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

$2 \frac{1}{x^{4} y^{3 \cdot 2}} x y^{2}$

Step 8.2.2

Multiply $3$ by $2$ .

$2 \frac{1}{x^{4} y^{6}} x y^{2}$

Step 9

Simplify terms.

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Step 9.1

Combine $2$ and $\frac{1}{x^{4} y^{6}}$ .

$\frac{2}{x^{4} y^{6}} x y^{2}$

Step 9.2

Cancel the common factor of $x$ .

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Step 9.2.1

Factor $x$ out of $x^{4} y^{6}$ .

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

Step 9.2.2

Cancel the common factor.

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

Step 9.2.3

Rewrite the expression.

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

Step 9.3

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

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Step 9.3.1

Factor $y^{2}$ out of $x^{3} y^{6}$ .

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

Step 9.3.2

Cancel the common factor.

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

Step 9.3.3

Rewrite the expression.

$\frac{2}{x^{3} y^{4}}$