Simplify (2x^2y*4x^4y^3)/(6x^6y^6)

$\frac{2 x^{2} y \cdot 4 x^{4} y^{3}}{6 x^{6} y^{6}}$

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

Move $x^{4}$ .

$\frac{2 (x^{4} x^{2}) y \cdot (4 y^{3})}{6 x^{6} y^{6}}$

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

$\frac{2 x^{4 + 2} y \cdot (4 y^{3})}{6 x^{6} y^{6}}$

Add $4$ and $2$ .

$\frac{2 x^{6} y \cdot (4 y^{3})}{6 x^{6} y^{6}}$

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

Move $y^{3}$ .

$\frac{2 x^{6} (y^{3} y) \cdot 4}{6 x^{6} y^{6}}$

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

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

$\frac{2 x^{6} (y^{3} y^{1}) \cdot 4}{6 x^{6} y^{6}}$

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

$\frac{2 x^{6} y^{3 + 1} \cdot 4}{6 x^{6} y^{6}}$

Add $3$ and $1$ .

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

Cancel the common factor of $2$ and $6$ .

Factor $2$ out of $2 x^{6} y^{4} \cdot 4$ .

$\frac{2 (x^{6} y^{4} \cdot 4)}{6 x^{6} y^{6}}$

Cancel the common factors.

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

$\frac{2 (x^{6} y^{4} \cdot 4)}{2 (3 x^{6} y^{6})}$

Cancel the common factor.

$\frac{2 (x^{6} y^{4} \cdot 4)}{2 (3 x^{6} y^{6})}$

Rewrite the expression.

$\frac{x^{6} y^{4} \cdot 4}{3 x^{6} y^{6}}$

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

Cancel the common factor.

$\frac{x^{6} y^{4} \cdot 4}{3 x^{6} y^{6}}$

Rewrite the expression.

$\frac{y^{4} \cdot 4}{3 y^{6}}$

Cancel the common factor of $y^{4}$ and $y^{6}$ .

Factor $y^{4}$ out of $y^{4} \cdot 4$ .

$\frac{y^{4} (4)}{3 y^{6}}$

Cancel the common factors.

Factor $y^{4}$ out of $3 y^{6}$ .

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

Cancel the common factor.

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

Rewrite the expression.

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