Question

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

Answer 1

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

Explanation:

`" "`

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:

`rArr [-15(1)(1)]/[5u^3*u]`

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

So, `u^3*u=u^3*u^1=u^4`

`rArr -[15]/[5u^4]`

`color(green)("Step 3 : "`

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

`rArr -(15/5)*(1/u^4)`

`rArr -(cancel 15^color(blue)(3)/cancel 5)*(1/u^4)`

`rArr -3*(1/u^4)`

`rArr -3/u^4`

Hence,

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