SOLUTION: (10/√5)^500 (1/(2√5))^500 =

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Question 230113: (10/√5)^500 (1/(2√5))^500 =
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
Since raising anything but 0 or 1 to the 500th power is difficult, even with a calculator, let's try to avoid doing that until the end. IOW we're going to simplify the expression in every way possible before we try to raise anything to the 500th power.

%2810%2Fsqrt%285%29%29%5E500%281%2F%282sqrt%285%29%29%29%5E500
We'll start by using the following property of exponents, a%5Ex%2Ab%5Ex+=+%28a%2Ab%29%5Ex to "undistribute" the exponent from the two fractions:
%28%2810%2Fsqrt%285%29%29%281%2F%282sqrt%285%29%29%29%29%5E500
Now we'll multiply the fractions:
%2810%2F%28sqrt%285%29%2A2sqrt%285%29%29%29%5E500
Next we'll use the Commutative and Associative Property of Multiplication to to group the sqrt%285%29's:
%2810%2F%28%28sqrt%285%29%2Asqrt%285%29%29%2A2%29%29%5E500
Since sqrt%285%29%2Asqrt%285%29+=+5:
%2810%2F%285%2A2%29%29%5E500
Simplifying the fraction
%2810%2F10%29%5E500
%281%29%5E500
And we now have something that is very easy to raise to the 500th power!
1%5E500+=+1