document.write( "Question 230113: (10/√5)^500 (1/(2√5))^500 = \n" ); document.write( "

Algebra.Com's Answer #170458 by jsmallt9(3758) $\"\"$ $\"About$

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.

\n" ); document.write( " $\"%2810%2Fsqrt%285%29%29%5E500%281%2F%282sqrt%285%29%29%29%5E500\"$
\n" ); document.write( "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:
\n" ); document.write( " $\"%28%2810%2Fsqrt%285%29%29%281%2F%282sqrt%285%29%29%29%29%5E500\"$
\n" ); document.write( "Now we'll multiply the fractions:
\n" ); document.write( " $\"%2810%2F%28sqrt%285%29%2A2sqrt%285%29%29%29%5E500\"$
\n" ); document.write( "Next we'll use the Commutative and Associative Property of Multiplication to to group the $\"sqrt%285%29\"$ 's:
\n" ); document.write( " $\"%2810%2F%28%28sqrt%285%29%2Asqrt%285%29%29%2A2%29%29%5E500\"$
\n" ); document.write( "Since $\"sqrt%285%29%2Asqrt%285%29+=+5\"$ :
\n" ); document.write( " $\"%2810%2F%285%2A2%29%29%5E500\"$
\n" ); document.write( "Simplifying the fraction
\n" ); document.write( " $\"%2810%2F10%29%5E500\"$
\n" ); document.write( " $\"%281%29%5E500\"$
\n" ); document.write( "And we now have something that is very easy to raise to the 500th power!
\n" ); document.write( " $\"1%5E500+=+1\"$
\n" ); document.write( " \n" ); document.write( "

\n" );