SOLUTION: (−4mn^6)(−5m^3n^2)^2 my answer was -100 m^10 n^10

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Question 712740: (−4mn^6)(−5m^3n^2)^2

my answer was
-100 m^10 n^10
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
Your error was in squaring %28-5m%5E3n%5E2%29%5E2. According to one rule of exponents, you raise a single term, like -5m%5E3n%5E2, to a power by raising each factor to that power. So according to this rule:
%28-5m%5E3n%5E2%29%5E2
becomes
%28-5%29%5E2%28m%5E3%29%5E2%28n%5E2%29%5E2
Squaring the -5 is easy. To square the powers of m and n we use another rule of exponents: Multiply the exponents! (This is where you went wrong. You apparently squared the 3 and got 9 and squared the 2 and got 4.) So we should get:
25m%5E6n%5E4
With %28-5m%5E3n%5E2%29%5E2 properly simplified to 25m%5E6n%5E4 we can now multiply it by -4mn%5E6 giving us:
-100m%5E7n%5E10

P.S. Your answer has n to the right power. But it is only a lucky accident that squaring the exponent of 2 (which you should not have done) works out the same as multiplying the exponents of 2 (which you should have done)!