Simplify (24x^3y^5)/(32x^7y^-9)

$\frac{24 x^{3} y^{5}}{32 x^{7} y^{- 9}}$

Move $y^{- 9}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{24 x^{3} y^{5} y^{9}}{32 x^{7}}$

Multiply $y^{5}$ by $y^{9}$ by adding the exponents.

Move $y^{9}$ .

$\frac{24 x^{3} (y^{9} y^{5})}{32 x^{7}}$

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

$\frac{24 x^{3} y^{9 + 5}}{32 x^{7}}$

Add $9$ and $5$ .

$\frac{24 x^{3} y^{14}}{32 x^{7}}$

Cancel the common factor of $24$ and $32$ .

Factor $8$ out of $24 x^{3} y^{14}$ .

$\frac{8 (3 x^{3} y^{14})}{32 x^{7}}$

Cancel the common factors.

Factor $8$ out of $32 x^{7}$ .

$\frac{8 (3 x^{3} y^{14})}{8 (4 x^{7})}$

Cancel the common factor.

$\frac{8 (3 x^{3} y^{14})}{8 (4 x^{7})}$

Rewrite the expression.

$\frac{3 x^{3} y^{14}}{4 x^{7}}$

Cancel the common factor of $x^{3}$ and $x^{7}$ .

Factor $x^{3}$ out of $3 x^{3} y^{14}$ .

$\frac{x^{3} (3 y^{14})}{4 x^{7}}$

Cancel the common factors.

Factor $x^{3}$ out of $4 x^{7}$ .

$\frac{x^{3} (3 y^{14})}{x^{3} (4 x^{4})}$

Cancel the common factor.

$\frac{x^{3} (3 y^{14})}{x^{3} (4 x^{4})}$

Rewrite the expression.

$\frac{3 y^{14}}{4 x^{4}}$