document.write( "Question 397063: the cubed root of 4x+1 to the 6th power \n" ); document.write( "

Algebra.Com's Answer #281553 by jsmallt9(3758) $\"\"$ $\"About$

You can put this solution on YOUR website!
Is it
\n" ); document.write( " $\"%28root%283%2C+4x%2B1%29%29%5E6\"$
\n" ); document.write( "or
\n" ); document.write( " $\"root%283%2C+%284x%2B1%29%5E6%29\"$ ?
\n" ); document.write( "In this particular expression it ends up not making any difference. But in other situations it may make a big difference. So please use parentheses to make things clear. Use
\n" ); document.write( "\"(the cubed root of 4x+1) to the 6th power\" for the first one
\n" ); document.write( "and
\n" ); document.write( "\"the cubed root of (4x+1 to the 6th power)\" for the second one. Tutors are more likely to help if the problem is clear.

\n" ); document.write( "A quick way to simplify this expression takes advantage of fractional exponents. The general pattern for the relationship between radical expressions and expressions using fractional exponents is:
\n" ); document.write( " $\"root%28a%2C+q%5Eb%29+=+%28root%28a%2C+q%29%29%5Eb+=+x%5E%28b%2Fa%29\"$
\n" ); document.write( "As you can see, both $\"%28root%283%2C+4x%2B1%29%29%5E6\"$ and $\"root%283%2C+%284x%2B1%29%5E6%29\"$ are both equal to:
\n" ); document.write( " $\"%284x%2B1%29%5E%286%2F3%29\"$
\n" ); document.write( "The exponent simplifies to a 2:
\n" ); document.write( " $\"%284x%2B1%29%5E2\"$
\n" ); document.write( "And last of all we can use FOIL or the $\"%28a%2Bb%29%5E2+=+a%5E2+%2B2ab+%2B+b%5E2\"$ pattern to square 4x+1. (I like using the pattern.)
\n" ); document.write( " $\"%284x%29%5E2+%2B+2%284x%29%281%29+%2B+%281%29%5E2\"$
\n" ); document.write( "which simplifies to:
\n" ); document.write( " $\"16x%5E2+%2B8x+%2B+1\"$
\n" ); document.write( "This is the simplified result for both $\"%28root%283%2C+4x%2B1%29%29%5E6\"$ and $\"root%283%2C+%284x%2B1%29%5E6%29\"$ . \n" ); document.write( "

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