# How do you simplify (-15w^0u^-1)/(5u^3)?

May 15, 2018

$\text{ }$
color(red)([-15w^0u^-1]/[5u^3] =-(3)/u^4

#### Explanation:

$\text{ }$

Given: color(blue)([-15w^0u^-1]/[5u^3]

color(green)("Step 1 : "

Exponent Rule: color(red)(m^0=1

So, color(blue)(w^0=1

Exponent Rule: color(red)(m^-n=1/m^n

So, color(blue)(u^-1=1/u^1=1/u

color(green)("Step 2 : "

Consider: color(blue)([-15w^0u^-1]/[5u^3]

To simplify, use the intermediate results found in Step 1:

$\Rightarrow \frac{- 15 \left(1\right) \left(1\right)}{5 {u}^{3} \cdot u}$

Exponent Rule: color(red)(a^m*a^n=a^(m+n)

So, ${u}^{3} \cdot u = {u}^{3} \cdot {u}^{1} = {u}^{4}$

$\Rightarrow - \frac{15}{5 {u}^{4}}$

color(green)("Step 3 : "

Combine color(red)("Like Terms" to simplify

$\Rightarrow - \left(\frac{15}{5}\right) \cdot \left(\frac{1}{u} ^ 4\right)$

$\Rightarrow - \left({\cancel{15}}^{\textcolor{b l u e}{3}} / \cancel{5}\right) \cdot \left(\frac{1}{u} ^ 4\right)$

$\Rightarrow - 3 \cdot \left(\frac{1}{u} ^ 4\right)$

$\Rightarrow - \frac{3}{u} ^ 4$

Hence,

color(blue)([-15w^0u^-1]/[5u^3] =-(3)/(u^4)