Simplify ((x^3y^2)(x^5y^7))/(x^2y^5)

$\frac{(x^{3} y^{2}) (x^{5} y^{7})}{x^{2} y^{5}}$

Multiply $x^{3}$ by $x^{5}$ by adding the exponents.

Move $x^{5}$ .

$\frac{x^{5} x^{3} y^{2} y^{7}}{x^{2} y^{5}}$

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

$\frac{x^{5 + 3} y^{2} y^{7}}{x^{2} y^{5}}$

Add $5$ and $3$ .

$\frac{x^{8} y^{2} y^{7}}{x^{2} y^{5}}$

Multiply $y^{2}$ by $y^{7}$ by adding the exponents.

Move $y^{7}$ .

$\frac{x^{8} (y^{7} y^{2})}{x^{2} y^{5}}$

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

$\frac{x^{8} y^{7 + 2}}{x^{2} y^{5}}$

Add $7$ and $2$ .

$\frac{x^{8} y^{9}}{x^{2} y^{5}}$

Cancel the common factor of $x^{8}$ and $x^{2}$ .

Factor $x^{2}$ out of $x^{8} y^{9}$ .

$\frac{x^{2} (x^{6} y^{9})}{x^{2} y^{5}}$

Cancel the common factors.

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

$\frac{x^{2} (x^{6} y^{9})}{x^{2} (y^{5})}$

Cancel the common factor.

$\frac{x^{2} (x^{6} y^{9})}{x^{2} y^{5}}$

Rewrite the expression.

$\frac{x^{6} y^{9}}{y^{5}}$

Cancel the common factor of $y^{9}$ and $y^{5}$ .

Factor $y^{5}$ out of $x^{6} y^{9}$ .

$\frac{y^{5} (x^{6} y^{4})}{y^{5}}$

Cancel the common factors.

Multiply by $1$ .

$\frac{y^{5} (x^{6} y^{4})}{y^{5} \cdot 1}$

Cancel the common factor.

$\frac{y^{5} (x^{6} y^{4})}{y^{5} \cdot 1}$

Rewrite the expression.

$\frac{x^{6} y^{4}}{1}$

Divide $x^{6} y^{4}$ by $1$ .

$x^{6} y^{4}$