Simplify (-15(y^2)^4)/(5y^3y^4)

$\frac{- 15 {(y^{2})}^{4}}{5 y^{3} y^{4}}$

Step 1

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

Move $y^{4}$ .

$\frac{- 15 {(y^{2})}^{4}}{5 (y^{4} y^{3})}$

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

$\frac{- 15 {(y^{2})}^{4}}{5 y^{4 + 3}}$

Add $4$ and $3$ .

$\frac{- 15 {(y^{2})}^{4}}{5 y^{7}}$

Step 2

Cancel the common factor of $- 15$ and $5$ .

Factor $5$ out of $- 15 {(y^{2})}^{4}$ .

$\frac{5 (- 3 {(y^{2})}^{4})}{5 y^{7}}$

Cancel the common factors.

Factor $5$ out of $5 y^{7}$ .

$\frac{5 (- 3 {(y^{2})}^{4})}{5 (y^{7})}$

Cancel the common factor.

$\frac{5 (- 3 {(y^{2})}^{4})}{5 y^{7}}$

Rewrite the expression.

$\frac{- 3 {(y^{2})}^{4}}{y^{7}}$

Step 3

Multiply the exponents in ${(y^{2})}^{4}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{- 3 y^{2 \cdot 4}}{y^{7}}$

Multiply $2$ by $4$ .

$\frac{- 3 y^{8}}{y^{7}}$

Step 4

Cancel the common factor of $y^{8}$ and $y^{7}$ .

Factor $y^{7}$ out of $- 3 y^{8}$ .

$\frac{y^{7} (- 3 y)}{y^{7}}$

Cancel the common factors.

Multiply by $1$ .

$\frac{y^{7} (- 3 y)}{y^{7} \cdot 1}$

Cancel the common factor.

$\frac{y^{7} (- 3 y)}{y^{7} \cdot 1}$

Rewrite the expression.

$\frac{- 3 y}{1}$

Divide $- 3 y$ by $1$ .

$- 3 y$