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

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

Step 1

Multiply $y^{4}$ by $y^{3}$ by adding the exponents.

Move $y^{3}$ .

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

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

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

Add $3$ and $4$ .

$\frac{2 y^{2}}{4 y^{7} \cdot 2}$

Step 2

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

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

$\frac{2 (y^{2})}{4 y^{7} \cdot 2}$

Cancel the common factors.

Factor $2$ out of $4 y^{7} \cdot 2$ .

$\frac{2 (y^{2})}{2 (2 y^{7} \cdot 2)}$

Cancel the common factor.

$\frac{2 y^{2}}{2 (2 y^{7} \cdot 2)}$

Rewrite the expression.

$\frac{y^{2}}{2 y^{7} \cdot 2}$

Step 3

Cancel the common factor of $y^{2}$ and $y^{7}$ .

Multiply by $1$ .

$\frac{y^{2} \cdot 1}{2 y^{7} \cdot 2}$

Cancel the common factors.

Factor $y^{2}$ out of $2 y^{7} \cdot 2$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 4

Multiply $2$ by $2$ .

$\frac{1}{4 y^{5}}$