SOLUTION: I have been struggling with this math problem for awhile now and I was wondering if anyone could help me? I would deeply appreciate it!! Please and Thank You!! Powers of Monomi

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Question 130954This question is from textbook Algebra Structure and Method
: I have been struggling with this math problem for awhile now and I was wondering if anyone could help me? I would deeply appreciate it!! Please and Thank You!!
Powers of Monomials
Find and simplify (a) the sum and (b) the product of the given monomials
(a^2)^6,(-2a^4)^3 This question is from textbook Algebra Structure and Method

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
First let's simplify the given monomials individually

%28a%5E2%29%5E6 Start with the first expression.


a%5E%282%2A6%29 Multiply the outer exponent with the inner exponent. Remember %28x%5Ey%29%5Ez=x%5E%28y%2Az%29


a%5E12 Now multiply the exponents


So %28a%5E2%29%5E6 simplifies to a%5E12.

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%28%28-2%29%5E1a%5E4%29%5E3 Start with the second expression. Note: %28-2a%5E4%29%5E3 really looks like %28%28-2%29%5E1a%5E4%29%5E3


%28-2%29%5E%281%2A3%29a%5E%284%2A3%29 Now distribute the outer exponent 3 to each exponent in the parenthesis. Remember %28x%5Ey%29%5Ez=x%5E%28y%2Az%29


%28-2%29%5E3a%5E12 Now multiply the exponents


-8a%5E12 Now raise -2 to the 3rd power to get -8

So %28-2a%5E4%29%5E3 simplifies to -8a%5E12.



a)


Now let's find the sum. To do that, simply add the two simplified expressions together


a%5E12%2B%28-8a%5E12%29


-7a%5E12 Combine like terms


So a%5E12 and -8a%5E12 add to -7a%5E12. In other words, a%5E12%2B%28-8a%5E12%29=-7a%5E12







b)


Now let's find the product. To do that, simply multiply the two simplified expressions together


%28a%5E12%29%28-8a%5E12%29


-8a%5E%2812%2B12%29 Add the exponents


-8a%5E24 Simplify


So a%5E12 and -8a%5E12 multiply to -8a%5E24. In other words, %28a%5E12%29%28-8a%5E12%29=-8a%5E24