Simplify Exponents and Confirm with Wolfram Alpha: (54-3y)3 * (5y-2)2 Solution

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DaleSwanson
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So I just got back from my math class, we were going over exponents. Right before we left he gave us a problem and we turned it in, I was just wondering if I got it right.

Simplify:
(54-3y)3 * (5y-2)2

I got:
512-9y3 * 5y2-4

5-9y3+y2+8

I applied the powers to the parenthesis, then added the two exponents. The addition of the exponents is here:
http://www.wolframalpha.com/input/?i=%2812-9y^3%29+%2B+%28y^2+-+4%29

However when I just pop the original problem into wolfram alpha I get:
http://www.wolframalpha.com/input/?i=%28%285^%284-3y%29%29^3%29+*+%28%285^%28y-2%29%29^2%29
58-7y

So I guess I have two questions. First is my answer right? Second how did Wolfram come up with that answer?
 

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You are applying the exponentiation rules incorrectly in your first step - perhaps you want to review it. When you bring down the 3, you multiply it to the (4-3y) to get (12-9y) instead of taking powers. Do the same for the other term. Then you can reduce the exponents.

See rules 3 here: http://mathworld.wolfram.com/ExponentLaws.html
 
Thanks. Stupid mistake, always the stupid mistakes.
 
That's fine - when you make mistakes you go back and look at the definitions, problems, and learn a lot that way. Cheers