SOLUTION: 1. Simplify and write the expression below using positive exponents only. (2u-3v2)-2

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Question 214121: 1. Simplify and write the expression below using positive exponents only.
(2u-3v2)-2

Answer by jim_thompson5910(21685) About Me  (Show Source):
You can put this solution on YOUR website!
Recall that x%5E%28-1%29=1%2Fx%5E1=1%2Fx and x%5E%28-2%29=1%2Fx%5E2. In other words, to rewrite an expression with positive exponents, just flip the base.


So in this case u%5E%28-3%29=1%2Fu%5E3. So 2u%5E%28-3%29v%5E2=2%281%2Fu%5E3%29v%5E2=%282v%5E2%29%2Fu%5E3


So %282u%5E%28-3%29v%5E2%29%5E%28-2%29=%28%282v%5E2%29%2Fu%5E3%29%5E%28-2%29



Now flip the fraction to make the outer exponent positive: %28%282v%5E2%29%2Fu%5E3%29%5E%28-2%29=%28%28u%5E3%29%2F%282v%5E2%29%29%5E2


Now simplify to get: %28%28u%5E3%29%2F%282v%5E2%29%29%5E2=%28u%5E6%29%2F%284v%5E4%29

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Answer:

So %282u%5E%28-3%29v%5E2%29%5E%28-2%29=%28u%5E6%29%2F%284v%5E4%29