Algebra Examples

${(x y)}^{- 3} (- x^{7} y^{2}) (30 x^{2})$

Step 1

Multiply $x^{7}$ by $x^{2}$ by adding the exponents.

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Step 1.1

Move $x^{2}$ .

${(x y)}^{- 3} (- (x^{2} x^{7}) y^{2}) \cdot 30$

Step 1.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

${(x y)}^{- 3} (- x^{2 + 7} y^{2}) \cdot 30$

Step 1.3

Add $2$ and $7$ .

${(x y)}^{- 3} (- x^{9} y^{2}) \cdot 30$

Step 2

Rewrite using the commutative property of multiplication.

$- {(x y)}^{- 3} x^{9} y^{2} \cdot 30$

Step 3

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

$- \frac{1}{{(x y)}^{3}} x^{9} y^{2} \cdot 30$

Step 4

Apply the product rule to $x y$ .

$- \frac{1}{x^{3} y^{3}} x^{9} y^{2} \cdot 30$

Step 5

Cancel the common factor of $x^{3}$ .

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Step 5.1

Move the leading negative in $- \frac{1}{x^{3} y^{3}}$ into the numerator.

$\frac{- 1}{x^{3} y^{3}} x^{9} y^{2} \cdot 30$

Step 5.2

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

$\frac{- 1}{x^{3} (y^{3})} x^{9} y^{2} \cdot 30$

Step 5.3

Factor $x^{3}$ out of $x^{9}$ .

$\frac{- 1}{x^{3} (y^{3})} (x^{3} x^{6}) y^{2} \cdot 30$

Step 5.4

Cancel the common factor.

$\frac{- 1}{x^{3} y^{3}} (x^{3} x^{6}) y^{2} \cdot 30$

Step 5.5

Rewrite the expression.

$\frac{- 1}{y^{3}} x^{6} y^{2} \cdot 30$

Step 6

Combine $\frac{- 1}{y^{3}}$ and $x^{6}$ .

$\frac{- x^{6}}{y^{3}} y^{2} \cdot 30$

Step 7

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

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Step 7.1

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

$\frac{- x^{6}}{y^{2} y} y^{2} \cdot 30$

Step 7.2

Cancel the common factor.

$\frac{- x^{6}}{y^{2} y} y^{2} \cdot 30$

Step 7.3

Rewrite the expression.

$\frac{- x^{6}}{y} \cdot 30$

Step 8

Move the negative in front of the fraction.

$- \frac{x^{6}}{y} \cdot 30$

Step 9

Multiply $- \frac{x^{6}}{y} \cdot 30$ .

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Step 9.1

Multiply $30$ by $- 1$ .

$- 30 \frac{x^{6}}{y}$

Step 9.2

Combine $- 30$ and $\frac{x^{6}}{y}$ .

$\frac{- 30 x^{6}}{y}$

Step 10

Move the negative in front of the fraction.

$- \frac{30 x^{6}}{y}$