SOLUTION: I am trying to help my son with an exponent question with an unknown exponent. Here is the sample question. (unfortunately it was not taken from a text book) Please Help me solv

Algebra ->  Exponents -> SOLUTION: I am trying to help my son with an exponent question with an unknown exponent. Here is the sample question. (unfortunately it was not taken from a text book) Please Help me solv      Log On


   



Question 69056: I am trying to help my son with an exponent question with an unknown exponent. Here is the sample question. (unfortunately it was not taken from a text book)
Please Help me solve this equation: 4n^x=4/n^2
I am trying to solve for x.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
4n%5Ex+=+4%2Fn%5E2
First, each side can be divided by 4
n%5Ex+=+1+%2F+n%5E2
Now multiply each side by n^2
n%5E2%2An%5Ex+=+1
The left side is similar to something like 5%5E2%2A5%5E3+=+5%5E%282%2B3%29
n%5E2%2A+n%5Ex+=+n%5E%282%2Bx%29
n%5E%282%2Bx%29+=+1
There is a rule that says "Anything raised to the zero power = 1"
So, stated backwards, "If something raised to an exponent = 1, then that
exponent must be zero"
2+%2B+x+=+0
x+=+-2
check:
4n%5Ex+=+4%2Fn%5E2
4n%5E%28-2%29+=+4%2Fn%5E2
multiply both sides by n%5E2
4n%5E%28-2%29%2An%5E2+=+4
4n%5E%28-2%2B2%29+=+4
4n%5E0+=+4
4%2A1+=+4
OK