document.write( "Question 398498: find the following 18 as the index square root of (-8)^18 \n" ); document.write( "

Algebra.Com's Answer #282512 by jsmallt9(3758) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"root%2818%2C+%28-8%29%5E18%29\"$
\n" ); document.write( "This is called \"the 18th root of $\"%28-8%29%5E18\"$ \". The phrase \"square root\" has nothing to do with this expression.

\n" ); document.write( "The 18th root of \"something\" is whatever expression you can raise to the 18th power to get that \"something\". So $\"root%2818%2C+%28-8%29%5E18%29\"$ is whatever expression you can raise to the 18th power to get $\"%28-8%29%5E18\"$ . The temptation would be to think that -8 to the 18th power results in $\"%28-8%29%5E18\"$ . But even-numbered roots, like 18th roots, are supposed to be positive. The simplified answer is just 8!. (If you think about it it should become clear that $\"%28-8%29%5E18\"$ and $\"%288%29%5E18\"$ will both work out to the the same (very large) number. So
\n" ); document.write( " $\"root%2818%2C+%28-8%29%5E18%29+=+8\"$
\n" ); document.write( " \n" ); document.write( "

\n" );