SOLUTION: Use the five properties of exponents to simplify each of the following expressions. (y^5)^3(y^3)^2 / (y^4)4

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Question 75667: Use the five properties of exponents to simplify each of the following expressions.
(y^5)^3(y^3)^2 / (y^4)4
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%28%28y%5E5%29%5E3%28y%5E3%29%5E2%29%2F%28y%5E4%29%5E4
When you raise a base with an exponent to an exponent, you multiply the exponents:
in other words,
%28x%5Ey%29%5Ez=x%5E%28y%2Az%29 So in our problem %28y%5E5%29%5E3=y%5E%283%2A5%29=y%5E15 and we do this for every exponent raised to an exponent
%28%28y%5E%285%2A3%29%29%28y%5E%283%2A2%29%29%29%2F%28y%5E%284%2A4%29%29
%28%28y%5E%2815%29%29%28y%5E%286%29%29%29%2F%28y%5E%2816%29%29
Now when you are multiplying like bases with exponents, you add the exponents ie x%5E2%2Ax%5E3=x%5E%282%2B3%29=x%5E5. So it becomes:
%28%28y%5E%2815%2B6%29%29%29%2F%28y%5E%2816%29%29
%28%28y%5E%2821%29%29%29%2F%28y%5E%2816%29%29
When you divide like bases with exponents you subtract the exponents ie x%5E3%2Fx%5E2=x%5E%283-2%29=x%5E1=x
y%5E%2821-16%29
y%5E%285%29
So the whole thing reduces down to y%5E5 in other words
%28%28y%5E5%29%5E3%28y%5E3%29%5E2%29%2F%28y%5E4%29%5E4=y%5E5