Question

Question #b143b

Answer 1

`1/5^(n+7)`

Explanation:

In order to simplify exponents, make sure that the bases are all the same. Change numbers to the product of their prime factors.

`(color(red)(25)^(2n-4))/(5^(3n+1) xx 5^(2n-3) xx 5) = (color(red)((5^2))^(2n-4))/(5^(3n+1) xx 5^(2n-3) xx 5)`

`=(color(red)(5)^(4n-8))/(5^(3n+1) xx 5^(2n-3) xx 5^1)`

Add the indices of like bases when multiplying

`(5^(4n-8))/(5^(5n-1)`

Method 1

Subtract the indices when dividing

`= 1/5^(5n-4n -1-(-8))`

`=1/5^(n+7)`

Method 2

`x^m = 1/(x^-m)`

`(5^(4n-8))/(5^(5n-1)`

`=1/(5^(5n-1) xx 5^(-4n+8))`

`=1/5^(n+7)`

Give the answer without negative or zero indices.