SOLUTION: Simplify. leave no negative exponents ONLY positive exponents (2m^3n)^2 (3m^-2n)

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Question 996847: Simplify. leave no negative exponents ONLY positive exponents
(2m^3n)^2 (3m^-2n)
Found 2 solutions by stanbon, Theo:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Simplify. leave no negative exponents ONLY positive exponents
(2m^3n)^2 (3m^-2n)
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(4m^6n^2)(3m^(-2)n)
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= 12m^(6-2)*n^3
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= 12*m^4*n^3
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Cheers,
Stan H.
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Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
this is clearer if it's written than if it's typed, so .....

$$$

i checked this by making m = 5 and n = 3 and evaluating the original expression and the final expression to see if they came up with the same answer.

they did which confirmed the solution was good.

basic concepts involved are:

(a^b)^c = a^(b*c)

(a^b * c^d)^e = a^(b*e) * c^(d*e)

for example:

(2^3)^2 = 2^(3*2) = 2^6
(2^3)^2 = 64 (original expression)
2^6 = 64 (final expression)

(2^3*3^4)^2 = 2^(3*2) * 3^(4*2) = 2^6 * 3^8
(2^3*3^4)^2 = 419904 (original expression)
2^^ * 3^8 = 419904 (final expression)

also:

a^b / a^c = a^(b-c)

for example:

2^5 / 2^3 = 2^(5-3) = 2^2
2^5 / 2^3 = 4 (original expression)
2^2 = 4 (final expression

here's a reference that should be helpful if you wish to take the time to read it.

http://www.wtamu.edu/academic/anns/mps/math/mathlab/beg_algebra/beg_alg_tut26_exp.htm