SOLUTION: I need to simplify ^3√128a^13b^6. Thank you.

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Question 844577: I need to simplify ^3√128a^13b^6. Thank you.
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!

The product of two powers with the same exponent
is a power where the product of the bases is raised to the same common exponent.
Similarly, the product of two roots with the same index
is the root with the same index of the product of the expressions inside each radical.
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
When simplifying you have to figure out the smarter way of factoring, and in
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
(The parts I am talking about are the coefficient (128), the power of a , and the power of b ).
b%5E6=b%5E%282%2A3%29=%28b%5E2%29%5E3 is a cube.
From the other parts I factored out the greatest cube I could factor out:
128=2%5E7=2%2A2%5E6=2%2A%282%5E3%29%5E3=2%2A4%5E3.
a%5E13=a%2Aa%5E12=a%2A%28a%5E4%29%5E3