Simplify ((x^5y^3)(x^9y^7))/(x^8y^4)

$\frac{(x^{5} y^{3}) (x^{9} y^{7})}{x^{8} y^{4}}$

Step 1

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

Move $x^{9}$ .

$\frac{x^{9} x^{5} y^{3} y^{7}}{x^{8} y^{4}}$

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

$\frac{x^{9 + 5} y^{3} y^{7}}{x^{8} y^{4}}$

Add $9$ and $5$ .

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

Step 2

Multiply $y^{3}$ by $y^{7}$ by adding the exponents.

Move $y^{7}$ .

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

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

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

Add $7$ and $3$ .

$\frac{x^{14} y^{10}}{x^{8} y^{4}}$

Step 3

Cancel the common factor of $x^{14}$ and $x^{8}$ .

Factor $x^{8}$ out of $x^{14} y^{10}$ .

$\frac{x^{8} (x^{6} y^{10})}{x^{8} y^{4}}$

Cancel the common factors.

Factor $x^{8}$ out of $x^{8} y^{4}$ .

$\frac{x^{8} (x^{6} y^{10})}{x^{8} (y^{4})}$

Cancel the common factor.

$\frac{x^{8} (x^{6} y^{10})}{x^{8} y^{4}}$

Rewrite the expression.

$\frac{x^{6} y^{10}}{y^{4}}$

Step 4

Cancel the common factor of $y^{10}$ and $y^{4}$ .

Factor $y^{4}$ out of $x^{6} y^{10}$ .

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

Cancel the common factors.

Multiply by $1$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

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

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