SOLUTION: Simplify the expressions by using the properties of rational exponents. Write the final answer using positive exponents only. (50p^-1q)^1/2 (this is the numerator) (2pq^-3)^1/

Algebra ->  Algebra  -> Real-numbers -> SOLUTION: Simplify the expressions by using the properties of rational exponents. Write the final answer using positive exponents only. (50p^-1q)^1/2 (this is the numerator) (2pq^-3)^1/      Log On

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Question 107733: Simplify the expressions by using the properties of rational exponents. Write the final answer using positive exponents only.
(50p^-1q)^1/2 (this is the numerator)
(2pq^-3)^1/2 (this is the denominator)

I don't have a clue. Please help.

Answer by solver91311(12126) About Me  (Show Source):
You can put this solution on YOUR website!
%28%2850p%5E%28-1%29q%29%5E%281%2F2%29%29%2F%282pq%5E%28-3%29%29%5E%281%2F2%29
Yes, indeed that is ugly. But fortunately, the exponent on the numerator and denominator is the same, so we can take this first step:

%28%2850p%5E%28-1%29q%29%2F%282pq%5E%28-3%29%29%29%5E%281%2F2%29

Now, any coefficient with a negative exponent can move from the numerator to the denominator, or vice versa, making the exponent positive. That's because of the rule a%5E%28-n%29=1%2F%28a%5En%29:

%28%2850q%5E4%29%2F%282p%5E2%29%29%5E%281%2F2%29

And then divide the 50 by the 2 in the denominator to get:

%28%2825q%5E4%29%2F%28p%5E2%29%29%5E%281%2F2%29

Finally, recall that a%5E%281%2F2%29=sqrt%28a%29. Applying this rule we get:

sqrt%28%2825q%5E4%29%2Fp%5E2%29=%28sqrt%2825q%5E4%29%29%2F%28sqrt%28p%5E2%29%29=%285q%5E2%29%2Fp