Algebra Examples

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

Step 1

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

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Step 1.1

Move $x$ .

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

Step 1.2

Multiply $x$ by $x^{- 2}$ .

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Step 1.2.1

Raise $x$ to the power of $1$ .

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

Step 1.2.2

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

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

Step 1.3

Subtract $2$ from $1$ .

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

Step 2

Multiply $y$ by $y^{- 3}$ by adding the exponents.

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Step 2.1

Move $y^{- 3}$ .

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

Step 2.2

Multiply $y^{- 3}$ by $y$ .

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Step 2.2.1

Raise $y$ to the power of $1$ .

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

Step 2.2.2

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

$3 x^{- 1} y^{- 3 + 1} \cdot - 2$

Step 2.3

Add $- 3$ and $1$ .

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

Step 3

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

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

Step 4

Combine $3$ and $\frac{1}{x}$ .

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

Step 5

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

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

Step 6

Combine.

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

Step 7

Multiply $3$ by $1$ .

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

Step 8

Multiply $\frac{3}{x y^{2}} \cdot - 2$ .

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Step 8.1

Combine $\frac{3}{x y^{2}}$ and $- 2$ .

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

Step 8.2

Multiply $3$ by $- 2$ .

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

Step 9

Move the negative in front of the fraction.

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