Simplify the following expression using positive exponents. (a^4b^-3)/(ab^-2)

Question

Simplify the following expression using positive exponents. (a^4b^-3)/(ab^-2)

 

I think the answer is a^3/b but I am a little confused on how to properly get there.

Answer 1

You're right, Danette.

a^4/a^1=a^(4-1)=a^3

b^(-3)/b^(-2)=b^(-3-[-2])=b^(-3+2)=b^(-1)=1/b

put them together to get a^3/b

another way to look at this is...

b^(-3)/b^(-2)=(1/b³)/(1/b²)=(1/b³)*(b²/1)=(b²/b³)=1/b

basically, b^(-3) in the numerator means b^3 goes into the denominator

also, b^(-2) in the denominator means b^2 goes into the numerator

b^2/b^3=1/b again if you want to remember it this way