Simplify (15x^6y^-9)/(5xy^-11)

$\frac{15 x^{6} y^{- 9}}{5 x y^{- 11}}$

Move $y^{- 11}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{15 x^{6} y^{- 9} y^{11}}{5 x}$

Multiply $y^{- 9}$ by $y^{11}$ by adding the exponents.

Move $y^{11}$ .

$\frac{15 x^{6} (y^{11} y^{- 9})}{5 x}$

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

$\frac{15 x^{6} y^{11 - 9}}{5 x}$

Subtract $9$ from $11$ .

$\frac{15 x^{6} y^{2}}{5 x}$

Cancel the common factor of $15$ and $5$ .

Factor $5$ out of $15 x^{6} y^{2}$ .

$\frac{5 (3 x^{6} y^{2})}{5 x}$

Cancel the common factors.

Factor $5$ out of $5 x$ .

$\frac{5 (3 x^{6} y^{2})}{5 (x)}$

Cancel the common factor.

$\frac{5 (3 x^{6} y^{2})}{5 x}$

Rewrite the expression.

$\frac{3 x^{6} y^{2}}{x}$

Cancel the common factor of $x^{6}$ and $x$ .

Factor $x$ out of $3 x^{6} y^{2}$ .

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

Cancel the common factors.

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

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

Factor $x$ out of $x^{1}$ .

$\frac{x (3 x^{5} y^{2})}{x \cdot 1}$

Cancel the common factor.

$\frac{x (3 x^{5} y^{2})}{x \cdot 1}$

Rewrite the expression.

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

Divide $3 x^{5} y^{2}$ by $1$ .

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