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

1 Answer
May 15, 2018

Answer:

#" "#
#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)#