Divide (5x^3y^9)/(20x^2y^-2)

$\frac{5 x^{3} y^{9}}{20 x^{2} y^{- 2}}$

Step 1

Move $y^{- 2}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{5 x^{3} y^{9} y^{2}}{20 x^{2}}$

Step 2

Multiply $y^{9}$ by $y^{2}$ by adding the exponents.

Move $y^{2}$ .

$\frac{5 x^{3} (y^{2} y^{9})}{20 x^{2}}$

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

$\frac{5 x^{3} y^{2 + 9}}{20 x^{2}}$

Add $2$ and $9$ .

$\frac{5 x^{3} y^{11}}{20 x^{2}}$

Step 3

Cancel the common factor of $5$ and $20$ .

Factor $5$ out of $5 x^{3} y^{11}$ .

$\frac{5 (x^{3} y^{11})}{20 x^{2}}$

Cancel the common factors.

Factor $5$ out of $20 x^{2}$ .

$\frac{5 (x^{3} y^{11})}{5 (4 x^{2})}$

Cancel the common factor.

$\frac{5 (x^{3} y^{11})}{5 (4 x^{2})}$

Rewrite the expression.

$\frac{x^{3} y^{11}}{4 x^{2}}$

Step 4

Cancel the common factor of $x^{3}$ and $x^{2}$ .

Factor $x^{2}$ out of $x^{3} y^{11}$ .

$\frac{x^{2} (x y^{11})}{4 x^{2}}$

Cancel the common factors.

Factor $x^{2}$ out of $4 x^{2}$ .

$\frac{x^{2} (x y^{11})}{x^{2} \cdot 4}$

Cancel the common factor.

$\frac{x^{2} (x y^{11})}{x^{2} \cdot 4}$

Rewrite the expression.

$\frac{x y^{11}}{4}$