document.write( "Question 147841: What would you do to simplify the 3rd root of 125^n*5^(4n)/25^-n without negative exponents and decimals in the final answer? \n" ); document.write( "

Algebra.Com's Answer #108268 by Fombitz(32388) $\"\"$ $\"About$

You can put this solution on YOUR website!
Remember exponentiation rules.
\n" ); document.write( " $\"x%5EM%2Ax%5EN=x%5E%28M%2BN%29\"$
\n" ); document.write( " $\"%28x%5EM%29%5EN=X%5E%28M%2AN%29\"$
\n" ); document.write( "Let's look at the individual terms first and make some simplifications.
\n" ); document.write( "125 and 25 are both divisible by 5.
\n" ); document.write( "Put them into lowest terms of base 5.
\n" ); document.write( " $\"125%5En=%285%5E3%29%5En\"$
\n" ); document.write( " $\"125%5En=5%5E%283n%29\"$
\n" ); document.write( ".
\n" ); document.write( ".
\n" ); document.write( ".
\n" ); document.write( " $\"25%5E%28-n%29=%285%5E2%29%5E%28-n%29\"$
\n" ); document.write( " $\"25%5E%28-n%29=5%5E%28-2n%29\"$
\n" ); document.write( " $\"25%5E%28-n%29=1%2F%285%5E%282n%29%29\"$
\n" ); document.write( " $\"1%2F%2825%5E%28-n%29%29=%285%5E%282n%29%29\"$
\n" ); document.write( ".
\n" ); document.write( ".
\n" ); document.write( ".\r
\n" ); document.write( "\n" ); document.write( "Now let's put it all together.
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\n" ); document.write( " $\"%28%28%28125%5En%29%285%5E%284n%29%29%29%2F%2825%5E%28-n%29%29%29%5E%281%2F3%29=5%5E%283n%29\"$ \r
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