Algebra Examples

${(- 7 x^{- 3} y)}^{2} \cdot 2 x^{- 4} y^{- 2}$

Step 1

Rewrite using the commutative property of multiplication.

$2 {(- 7 x^{- 3} y)}^{2} x^{- 4} y^{- 2}$

Step 2

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

$2 {(- 7 \frac{1}{x^{3}} y)}^{2} x^{- 4} y^{- 2}$

Step 3

Combine $- 7$ and $\frac{1}{x^{3}}$ .

$2 {(\frac{- 7}{x^{3}} y)}^{2} x^{- 4} y^{- 2}$

Step 4

Move the negative in front of the fraction.

$2 {(- \frac{7}{x^{3}} y)}^{2} x^{- 4} y^{- 2}$

Step 5

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

$2 {(- \frac{y \cdot 7}{x^{3}})}^{2} x^{- 4} y^{- 2}$

Step 6

Move $7$ to the left of $y$ .

$2 {(- \frac{7 \cdot y}{x^{3}})}^{2} x^{- 4} y^{- 2}$

Step 7

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

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Step 7.1

Apply the product rule to $- \frac{7 y}{x^{3}}$ .

$2 ({(- 1)}^{2} {(\frac{7 y}{x^{3}})}^{2}) x^{- 4} y^{- 2}$

Step 7.2

Apply the product rule to $\frac{7 y}{x^{3}}$ .

$2 ({(- 1)}^{2} \frac{{(7 y)}^{2}}{{(x^{3})}^{2}}) x^{- 4} y^{- 2}$

Step 7.3

Apply the product rule to $7 y$ .

$2 ({(- 1)}^{2} \frac{7^{2} y^{2}}{{(x^{3})}^{2}}) x^{- 4} y^{- 2}$

Step 8

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

$2 (1 \frac{7^{2} y^{2}}{{(x^{3})}^{2}}) x^{- 4} y^{- 2}$

Step 9

Multiply $\frac{7^{2} y^{2}}{{(x^{3})}^{2}}$ by $1$ .

$2 \frac{7^{2} y^{2}}{{(x^{3})}^{2}} x^{- 4} y^{- 2}$

Step 10

Raise $7$ to the power of $2$ .

$2 \frac{49 y^{2}}{{(x^{3})}^{2}} x^{- 4} y^{- 2}$

Step 11

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

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Step 11.1

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

$2 \frac{49 y^{2}}{x^{3 \cdot 2}} x^{- 4} y^{- 2}$

Step 11.2

Multiply $3$ by $2$ .

$2 \frac{49 y^{2}}{x^{6}} x^{- 4} y^{- 2}$

Step 12

Multiply $2 \frac{49 y^{2}}{x^{6}}$ .

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Step 12.1

Combine $2$ and $\frac{49 y^{2}}{x^{6}}$ .

$\frac{2 (49 y^{2})}{x^{6}} x^{- 4} y^{- 2}$

Step 12.2

Multiply $49$ by $2$ .

$\frac{98 y^{2}}{x^{6}} x^{- 4} y^{- 2}$

Step 13

Cancel the common factor of $x^{- 4}$ .

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Step 13.1

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

$\frac{98 y^{2}}{x^{- 4} x^{10}} x^{- 4} y^{- 2}$

Step 13.2

Cancel the common factor.

$\frac{98 y^{2}}{x^{- 4} x^{10}} x^{- 4} y^{- 2}$

Step 13.3

Rewrite the expression.

$\frac{98 y^{2}}{x^{10}} y^{- 2}$

Step 14

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

$\frac{98 y^{2}}{x^{10}} \cdot \frac{1}{y^{2}}$

Step 15

Combine.

$\frac{98 y^{2} \cdot 1}{x^{10} y^{2}}$

Step 16

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

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Step 16.1

Cancel the common factor.

$\frac{98 y^{2} \cdot 1}{x^{10} y^{2}}$

Step 16.2

Rewrite the expression.

$\frac{98 \cdot 1}{x^{10}}$

Step 17

Multiply $98$ by $1$ .

$\frac{98}{x^{10}}$