What are the cases?

Question

What are the cases when
1^(2n+3)=1^(3n-2)?

Answer 1

The above statement is true for all values of 'n' IF 'n' IS AN INTEGER and is not true if nis a fraction cause 1^(1/3) has 3 values and so if n is a fraction it would have n values of which one is 1

Answer 2

all n are ok.
This can be seen as follows :
take the log at both sides. This is allowed because both sides are always positive.
you will get then :

(2n+3) log (1) = (3n-2) log(1)

the log(1) = 0 , so n doesnt matter

another way of looking at it is the following

Define two epsilon-balloons around the 1^(2n+3) and 1^(3n-2)
Put a needle in both , and let them go to zero , now make the remarque that a balloon with a hole in it is topologicly equivalent with an interval , since both o=goes the zero the limit exists and is eqaul independent of the n-value. this concludes the poof

Answer 3

All cases!
1^(anything) = 1

but if you'd like to take it one step further, then that actually means that 2n+3=3n-2

solve for n;
3n-2n = 3-2
n=1;

This answer would only make a difference if the base was something other than 1.

Answer 4

Thta the same 1 * 1 (n-times, n from 1 to no end) is 1. That's Algebra!

Answer 5

the cases are when n belongs to the set of real numbers. I'm not sure about imaginary numbers.

Answer 6

the equation is right, when n is substituted, the result is same.