specialxknc wrote:

When i worked this problem I did the following:

5^12 -> 5*5^11 but why is 5*5^11 not equal 25^11?

I am stuck on this part, and im sure it is simply to do with order of operations but i cant wrap my mind around it.

5*5^11 = 5^1 * 5^11 = 5*(1+11)

25^11 = (5^2)^11 = 5^(2*11) = 5^22

Rules for exponents are as follows:

(1) \(x^m * x^n = x^(m+n)\)

(2) \(x^m / x^n = x^(m-n)\)

(3) \(x^(-m)\) = \(1/x^m\)

(4) \(x^0\) =1

(5) \((x^m)^n\) = \(x^(mn)\)

(6) \(x^m * y^m\) = \((xy)^m\)