Question

Evaluate:

`(4^(n + 4) - 5 xx 4^(n + 2))/(4^(n + 1) xx 11)`

Answer 1

Given expression is `(4^(n + 4) - 5 xx 4^(n + 2))/(4^(n + 1) xx 11)`

Using the laws of exponents that is `a^(n + m) = a^n xx a^m` we get,

= `(4^n xx 4^4 - 5 xx 4^n xx 4^2)/(4^n xx 4^1 xx 11)`

Now, taking out the common term and simplifying the expression by cancelling out the same term we get,

= `(4^n(4^4 - 5 xx 4^2))/(4^n xx 4^1 xx 11)`

= `(4^4 - 5 xx 4^2)/(4 xx 11)`

= `(4(4^3 - 5 xx 4))/(4 xx 11)`

= `(64 - 20)/11`

= `44/11`

= 4

Therefore, the value of `(4^(n + 4) - 5 xx 4^(n + 2))/(4^(n + 1) xx 11) = 4`