SOLUTION: If (y^2) x (y^a) = y^8 and (y^2)^b= (y^12) what is a + b? Thanks!

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Question 643377: If (y^2) x (y^a) = y^8 and (y^2)^b= (y^12) what is a + b? Thanks!
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
what is a+%2B+b?
Whenever you multiply two terms with the same base, you can add the exponents:
%28+x%5E+m+%29%28+x%5E+n+%29+=+x%5E%28+m+%2B+n+%29
so, you have:
%28y%5E2%29+%2A%28y%5Ea%29+=+y%5E8 ...=>...if bases are equal, then exponents are equal too
y%5E%282%2Ba%29+=+y%5E8...=>...2%2Ba=8=>...a=8-2=>...highlight%28a=6%29
and
-Whenever you have an exponent expression that is raised to a power, you can multiply the exponent and power:
%28+x%5Em+%29%5En+=+x%5E%28+m+n%29
so, you have:
%28y%5E2%29%5Eb=+y%5E12 ...=>...%28y%5E%282b%29%29=+y%5E12...=>...2b=+12...=>...highlight%28b=+6%29
a+%2B+b=6%2B6=12