Question 230113
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.<br>
{{{(10/sqrt(5))^500(1/(2sqrt(5)))^500}}}
We'll start by using the following property of exponents, {{{a^x*b^x = (a*b)^x}}} to "undistribute" the exponent from the two fractions:
{{{((10/sqrt(5))(1/(2sqrt(5))))^500}}}
Now we'll multiply the fractions:
{{{(10/(sqrt(5)*2sqrt(5)))^500}}}
Next we'll use the Commutative and Associative Property of Multiplication to to group the {{{sqrt(5)}}}'s:
{{{(10/((sqrt(5)*sqrt(5))*2))^500}}}
Since {{{sqrt(5)*sqrt(5) = 5}}}:
{{{(10/(5*2))^500}}}
Simplifying the fraction
{{{(10/10)^500}}}
{{{(1)^500}}}
And we now have something that is very easy to raise to the 500th power!
{{{1^500 = 1}}}