(x^7a)^a-b / (x^3a)^a-2b

Question

Expand and simplify the following powers. Give all of the answers in terms of positive exponents.

 

(x^7a)^a-b / (x^3a)^a-2b

 

Please help, and explain on how to get the answer. I've spent a long time trying to figure this out

 

Thanks.

Answer 1

An expression of the form (x^m)ⁿ can be re-written as x^mn

 

Therefore we have 

 

x^7a²-7ab ÷ x^3a²-6ab

 

When we divide like bases, we subtract the exponents. Here, we have a common base of x.

 

So we have

 

x^{7a² - 7ab - (3a²-6ab)}

 

= x^4a²-ab

 

or x^4a²/x^ab