Question

Simplify:

`(4^(3n) + 4^(2n) * 4^(n + 1))/((4 xx 4^n)^3 - 4 xx 4^(3n))`

Answer 1

`(4^(3n) + 4^(2n) * 4^(n + 1))/((4 xx 4^n)^3 - 4 xx 4^(3n))`

= `(4^(3n) + 4^(3n + 1))/(4^(3(n + 1)) - 4^(3n + 1))`

= `(4^(3n)(1 + 4))/(4^(3n + 1)(4^2 - 1))`

= `(5 * 4^(3n))/(4^(3n + 1) * 15)`

= `5/(15 * 4)`

= `1/12`