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

1 Answer
Dec 19, 2016

(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