Simplify (4x^2y)/(2xz^2)*(6xz^3)/(20y^4)

$\frac{4 x^{2} y}{2 x z^{2}} \cdot \frac{6 x z^{3}}{20 y^{4}}$

Combine.

$\frac{4 x^{2} y (6 x z^{3})}{2 x z^{2} (20 y^{4})}$

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

Move $x$ .

$\frac{4 (x \cdot x^{2}) y (6 z^{3})}{2 x z^{2} (20 y^{4})}$

Multiply $x$ by $x^{2}$ .

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

$\frac{4 (x^{1} x^{2}) y (6 z^{3})}{2 x z^{2} (20 y^{4})}$

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

$\frac{4 x^{1 + 2} y (6 z^{3})}{2 x z^{2} (20 y^{4})}$

Add $1$ and $2$ .

$\frac{4 x^{3} y (6 z^{3})}{2 x z^{2} (20 y^{4})}$

Cancel the common factor of $4$ and $2$ .

Factor $2$ out of $4 x^{3} y (6 z^{3})$ .

$\frac{2 (2 x^{3} y (6 z^{3}))}{2 x z^{2} (20 y^{4})}$

Cancel the common factors.

Factor $2$ out of $2 x z^{2} (20 y^{4})$ .

$\frac{2 (2 x^{3} y (6 z^{3}))}{2 (x z^{2} (20 y^{4}))}$

Cancel the common factor.

$\frac{2 (2 x^{3} y (6 z^{3}))}{2 (x z^{2} (20 y^{4}))}$

Rewrite the expression.

$\frac{2 x^{3} y (6 z^{3})}{x z^{2} (20 y^{4})}$

Cancel the common factor of $2$ and $20$ .

Factor $2$ out of $2 x^{3} y (6 z^{3})$ .

$\frac{2 (x^{3} y (6 z^{3}))}{x z^{2} (20 y^{4})}$

Cancel the common factors.

Factor $2$ out of $x z^{2} (20 y^{4})$ .

$\frac{2 (x^{3} y (6 z^{3}))}{2 (x z^{2} (10 y^{4}))}$

Cancel the common factor.

$\frac{2 (x^{3} y (6 z^{3}))}{2 (x z^{2} (10 y^{4}))}$

Rewrite the expression.

$\frac{x^{3} y (6 z^{3})}{x z^{2} (10 y^{4})}$

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

Factor $x$ out of $x^{3} y (6 z^{3})$ .

$\frac{x (x^{2} y (6 z^{3}))}{x z^{2} (10 y^{4})}$

Cancel the common factors.

Factor $x$ out of $x z^{2} (10 y^{4})$ .

$\frac{x (x^{2} y (6 z^{3}))}{x (z^{2} (10 y^{4}))}$

Cancel the common factor.

$\frac{x (x^{2} y (6 z^{3}))}{x (z^{2} (10 y^{4}))}$

Rewrite the expression.

$\frac{x^{2} y (6 z^{3})}{z^{2} (10 y^{4})}$

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

Factor $y$ out of $x^{2} y (6 z^{3})$ .

$\frac{y (x^{2} (6 z^{3}))}{z^{2} (10 y^{4})}$

Cancel the common factors.

Factor $y$ out of $z^{2} (10 y^{4})$ .

$\frac{y (x^{2} (6 z^{3}))}{y (z^{2} (10 y^{3}))}$

Cancel the common factor.

$\frac{y (x^{2} (6 z^{3}))}{y (z^{2} (10 y^{3}))}$

Rewrite the expression.

$\frac{x^{2} (6 z^{3})}{z^{2} (10 y^{3})}$

Cancel the common factor of $6$ and $10$ .

Factor $2$ out of $x^{2} (6 z^{3})$ .

$\frac{2 (x^{2} (3 z^{3}))}{z^{2} (10 y^{3})}$

Cancel the common factors.

Factor $2$ out of $z^{2} (10 y^{3})$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $z^{3}$ and $z^{2}$ .

Factor $z^{2}$ out of $x^{2} (3 z^{3})$ .

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

Cancel the common factors.

Cancel the common factor.

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

Rewrite the expression.

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

Move $3$ to the left of $x^{2}$ .

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

Simplify (4x^2y)/(2xz^2)*(6xz^3)/(20y^4)

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