# How do you divide (24x^2y^2) / (14x^3y^7)?

Jul 9, 2015

$\frac{24 {x}^{2} {y}^{2}}{14 {x}^{3} {y}^{7}} = \frac{12}{7 x {y}^{5}}$

#### Explanation:

$\frac{24 {x}^{2} {y}^{2}}{14 {x}^{3} {y}^{7}}$

$\textcolor{w h i t e}{\text{XXXX}}$$= \textcolor{red}{\left(\frac{24}{14}\right)} \cdot \textcolor{b l u e}{\left(\frac{{x}^{2}}{{x}^{3}}\right)} \cdot \textcolor{g r e e n}{\left(\frac{{y}^{2}}{{y}^{7}}\right)}$

$\textcolor{w h i t e}{\text{XXXX}}$$= \textcolor{red}{\left(\frac{12}{7}\right)} \cdot \textcolor{b l u e}{\left(\frac{1}{x}\right)} \cdot \textcolor{g r e e n}{\left(\frac{1}{y} ^ 5\right)}$

$\textcolor{w h i t e}{\text{XXXX}}$$= \frac{12}{7 x {y}^{5}}$

Jul 9, 2015

Simplify $\frac{24}{14}$ to $\frac{12}{7}$ by dividing by $2$. Apply the quotient rule and negative power rule of exponents.

#### Explanation:

$\frac{24 {x}^{2} {y}^{2}}{14 {x}^{3} {y}^{7}}$

Divide the numerator and denominator by $2$.

$\frac{12 {x}^{2} {y}^{2}}{7 {x}^{3} {y}^{7}}$

Apply the exponent quotient rule: ${x}^{a} / {x}^{b} = {x}^{a} - b$.

$\frac{12 {x}^{2 - 3} {y}^{2 - 7}}{7}$ =

$\frac{12 {x}^{- 1} {y}^{- 5}}{7}$ =

Apply the exponent negative power rule: ${x}^{-} a = \frac{1}{x} ^ a$.

$\frac{12}{7 {x}^{1} {y}^{5}}$ =

$\frac{12}{7 x {y}^{5}}$