Simplify ((x^2y)(x^4y^3))/(xy^2)

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

Step 1

Multiply $x^{2}$ by $x^{4}$ by adding the exponents.

Move $x^{4}$ .

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

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

$\frac{x^{4 + 2} y \cdot y^{3}}{x y^{2}}$

Add $4$ and $2$ .

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

Step 2

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

Move $y^{3}$ .

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

Multiply $y^{3}$ by $y$ .

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

$\frac{x^{6} (y^{3} y^{1})}{x y^{2}}$

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

$\frac{x^{6} y^{3 + 1}}{x y^{2}}$

Add $3$ and $1$ .

$\frac{x^{6} y^{4}}{x y^{2}}$

Step 3

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

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

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

Cancel the common factors.

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

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{x^{5} y^{4}}{y^{2}}$

Step 4

Cancel the common factor of $y^{4}$ and $y^{2}$ .

Factor $y^{2}$ out of $x^{5} y^{4}$ .

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

Cancel the common factors.

Multiply by $1$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

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

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