document.write( "Question 844577: I need to simplify ^3√128a^13b^6. Thank you. \n" ); document.write( "

Algebra.Com's Answer #508855 by KMST(5328) $\"\"$ $\"About$

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\n" ); document.write( "The product of two powers with the same exponent
\n" ); document.write( "is a power where the product of the bases is raised to the same common exponent.
\n" ); document.write( "Similarly, the product of two roots with the same index
\n" ); document.write( "is the root with the same index of the product of the expressions inside each radical.
\n" ); document.write( "So, $\"root%283%2C64%2Aa%5E12%2Ab%5E6%29%2Aroot%283%2C2a%29\"$ = $\"root%283%2C%2864%2Aa%5E12%2Ab%5E6%29%2A%282a%29%29\"$ = $\"root%283%2C2%2A64%2Aa%2Aa%5E12%2Ab%5E6%29\"$
\n" ); document.write( "When simplifying you have to figure out the smarter way of factoring, and in
\n" ); document.write( " $\"128%2Aa%5E13%2Ab%5E6=2%2A64%2Aa%2Aa%5E12%2Ab%5E6\"$ I factored cubes out of each part/factor in $\"128%2Aa%5E13%2Ab%5E6\"$
\n" ); document.write( "(The parts I am talking about are the coefficient (128), the power of $\"a\"$ , and the power of $\"b\"$ ).
\n" ); document.write( " $\"b%5E6=b%5E%282%2A3%29=%28b%5E2%29%5E3\"$ is a cube.
\n" ); document.write( "From the other parts I factored out the greatest cube I could factor out:
\n" ); document.write( " $\"128=2%5E7=2%2A2%5E6=2%2A%282%5E3%29%5E3=2%2A4%5E3\"$ .
\n" ); document.write( " $\"a%5E13=a%2Aa%5E12=a%2A%28a%5E4%29%5E3\"$ \n" ); document.write( "

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