Question

How do you evaluate `\frac { 3^ { 6} - 3^ { 2} } { 9^ { 4} - 9^ { 2} }`?

Answer 1

`(3^6-3^2)/(9^4-9^2) = 1/9`

Explanation:

`(3^6-3^2)/(9^4-9^2) = (3^2(3^4-1))/(9^2(9^2-1))`

`color(white)((3^6-3^2)/(9^4-9^2)) = (3^2color(red)(cancel(color(black)((3^4-1)))))/(3^4color(red)(cancel(color(black)((3^4-1)))))`

`color(white)((3^6-3^2)/(9^4-9^2)) = 3^2/3^4`

`color(white)((3^6-3^2)/(9^4-9^2)) = 1/3^2`

`color(white)((3^6-3^2)/(9^4-9^2)) = 1/9`