SOLUTION: Please Help Me Solve This Problem: Simplify Each: y^-7 Thank you for your time and help !

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Question 22969: Please Help Me Solve This Problem:
Simplify Each:
y^-7
Thank you for your time and help !

Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
Have you done anything with the laws of exponents? For example, when you divide with the same base number, you subtract exponents:
%28x%5E12%29%2F%28x%5E5%29=+x%5E7+

If it had been %28x%5E5%29%2F%28x%5E12%29 can you see that if you subtract exponents you would have x%5E%285-12%29 which could be written x%5E%28-7%29?

This same problem %28x%5E5%29%2F%28x%5E12%29 could also be simplified as a fraction to be reduced by dividing out the five x factors in the numerator with five of the x factors in the denominator. In this method, all the x factors in the numerator divide out, and you would be left with a 1 in the numerator since they all divided out and seven factors of x left in the denominator:
1%2Fx%5E7

What you have just done is derived the formula x%5E%28-7%29=+1%2F%28x%5E7%29

In summary, any time you have a negative exponent, you get a fraction whose numerator is 1, and whose denominator is the same as the original problem but with a positive exponent. For examples:
x%5E%28-2%29=+1%2F%28x%5E2%29

x%5E%28-3%29=+1%2F%28x%5E3%29

R^2 at SCC