Algebra Examples

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

Step 1

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

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Step 1.1

Move $x^{- 2}$ .

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

Step 1.2

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

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

Step 1.3

Add $- 2$ and $2$ .

$- x^{0} y^{- 3} \cdot y^{2}$

Step 2

Simplify $- x^{0} y^{- 3} \cdot y^{2}$ .

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

Step 3

Multiply $y^{- 3}$ by $y^{2}$ by adding the exponents.

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Step 3.1

Move $y^{2}$ .

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

Step 3.2

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

$- 1 y^{2 - 3}$

Step 3.3

Subtract $3$ from $2$ .

$- 1 y^{- 1}$

Step 4

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

$- 1 \frac{1}{y}$

Step 5

Rewrite $- 1 \frac{1}{y}$ as $- \frac{1}{y}$ .

$- \frac{1}{y}$