Precalculus Examples

$\frac{5 x y^{- 2}}{x^{- 1} y^{- 3}}$

Step 1

Move $x^{- 1}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{5 x y^{- 2} x}{y^{- 3}}$

Step 2

Move $y^{- 3}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$5 x y^{- 2} x y^{3}$

Step 3

Multiply $x$ by $x$ by adding the exponents.

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Step 3.1

Move $x$ .

$5 (x \cdot x) y^{- 2} y^{3}$

Step 3.2

Multiply $x$ by $x$ .

$5 x^{2} y^{- 2} y^{3}$

Step 4

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

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Step 4.1

Move $y^{3}$ .

$5 x^{2} (y^{3} y^{- 2})$

Step 4.2

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

$5 x^{2} y^{3 - 2}$

Step 4.3

Subtract $2$ from $3$ .

$5 x^{2} y^{1}$

Step 5

Simplify $5 x^{2} y^{1}$ .

$5 x^{2} y$