Question

Evaluate:

`(7^(n + 2) - 9 xx 7^n)/(7^(n + 1) xx 5)`

Answer 1

Given expression is `(7^(n + 2) - 9 xx 7^n)/(7^(n + 1) xx 5)`

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

= `(7^n xx 7^2 - 9 xx 7^n)/(7^n xx 7^1 xx 5)`

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

= `(7^n7^2 - 9)/(7^n xx 7^1 xx 5)`

= `(49 - 9)/35`

= `40/35`

= `8/7`

Therefore, the value of `(7^(n + 2) - 9 xx 7^n)/(7^(n + 1) xx 5)` is `8/7`.