SOLUTION: Simplify 9squared x 2cubed x 3square root 2 x 27 negative2 by writting as powers of prime factors. Thank you in advance.

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Question 811770: Simplify 9squared x 2cubed x 3square root 2 x 27 negative2 by writting as powers of prime factors.
Thank you in advance.
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
I am not sure what you meant, but here are 2 interpretations

%289%5E2%29%282%5E3%29%283sqrt%282%29%29%2827%29%28-2%29 = %28%283%5E2%29%5E2%29%282%5E3%29%283%2A2%5E0.5%29%283%5E3%29%28-2%29
= -%283%5E4%29%282%5E3%29%283%2A2%5E0.5%29%283%5E3%29%282%29
= -%283%5E4%29%282%5E3%29%283%29%282%5E0.5%29%283%5E3%29%282%29 = -%282%5E3%2A2%2A2%5E0.5%29%283%5E4%2A3%2A3%5E3%29
= -%282%5E%283%2B1%2B0.5%29%29%283%5E%284%2B1%2B3%29%29 = -2%5E4.5%2A3%5E8

%289%5E2%29%282%5E3%29%283sqrt%282%29%29%2827%5E%28-2%29%29 = %28%283%5E2%29%5E2%29%282%5E3%29%283%2A2%5E0.5%29%28%283%5E3%29%5E%28-2%29%29
= %283%5E4%29%282%5E3%29%283%2A2%5E0.5%29%283%5E%28-6%29%29 = %282%5E3%2A2%5E0.5%29%283%5E4%2A3%2A3%5E%28-6%29%29
= 2%5E3.5%2A3%5E%284%2B1-6%29 = 2%5E3.5%2A3%5E%28-1%29 = 2%5E3sqrt%282%29%2F3

I had to write 2%5E0.5} with 0.5 as an exponent instead of 1%2F2
because 2%5E%281%2F2%29 does not show properly.

NOTE: You can write 2^3 for 2%5E3 and sqrt(2) for sqrt%282%29 and we will understand it. Those are common ways to write exponents and square roots.
Other roots, like root%283%2C27%29 are trickier. Although many of us would recognize "root(3,27)" as meaning root%283%2C27%29, that is not as commonly understood.