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

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Answer 1 · 2018-05-15T09:02:01

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

$" "$

**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,

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

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