# How do you simplify (14y^3)/(7y)?

Jun 6, 2018

(14y^3)/(7y)=color(blue)(2y^2

#### Explanation:

Simplify:

$\frac{14 {y}^{3}}{7 y}$

Apply quotient rule of exponents: ${a}^{m} / {a}^{n} = {a}^{m - n}$

$\frac{14 {y}^{3 - 1}}{7}$

$\frac{14 {y}^{2}}{7}$

Simplify $\frac{14}{7}$ to $2$.

$2 {y}^{2}$

Jun 6, 2018

$2 {y}^{2}$

#### Explanation:

$\frac{14 {y}^{3}}{7 y}$

first use Commutative Property:

$\frac{a b}{c d} = \frac{a}{c} \cdot \frac{b}{d}$:

$\frac{14 {y}^{3}}{7 y} = \frac{14}{7} \cdot {y}^{3} / y = 2 \cdot {y}^{3} / y$

now use the Quotient Rule of Exponents:

${a}^{n} / {a}^{m} = {a}^{n - m}$ and realize that $y = {y}^{1}$

$2 \cdot {y}^{3} / y = 2 \cdot {y}^{3} / {y}^{1} = 2 \cdot {y}^{3 - 1} = 2 {y}^{2}$