SOLUTION: (8B^6)^4/3 OVER (64a^12)^1/6 PLEASE!!!!!!!!!!! STEP BY STEP!!

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Question 175710: (8B^6)^4/3 OVER (64a^12)^1/6 PLEASE!!!!!!!!!!! STEP BY STEP!!
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
%28%288b%5E6%29%5E%284%2F3%29%29+%2F+%28%2864a%5E12%29%5E%281%2F6%29%29
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First you need the general concept
%28a%5E5%29%5E3+=+a%5E5+%2A+a%5E5+%2A+a%5E5
a%5E5+%2A+a%5E5+%2A+a%5E5+=+a%5E15
So, when you see something like this, you multiply
the exponents
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%28%288b%5E6%29%5E%284%2F3%29%29+%2F+%28%2864a%5E12%29%5E%281%2F6%29%29
next
%288b%29%5E%286%2A%284%2F3%29%29+%2F+%2864a%29%5E%2812%2A%281%2F6%29%29
--------------
Now you need the general concept
%28a%2Ab%29%5E5+=+%28a%2Ab%29%2A%28a%2Ab%29%2A%28a%2Ab%29%2A%28a%2Ab%29%2A%28a%2Ab%29
next
%28a%2Ab%29%2A%28a%2Ab%29%2A%28a%2Ab%29%2A%28a%2Ab%29%2A%28a%2Ab%29+=+a%5E5%2Ab%5E5
--------------
%288b%29%5E%286%2A%284%2F3%29%29+%2F+%2864a%29%5E%2812%2A%281%2F6%29%29
next
%288b%29%5E%288%29+%2F+%2864a%29%5E%282%29
next
%288%5E8%29%2A%28b%5E8%29+%2F+%28%2864%5E2%29%2A%28a%5E2%29%29
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Now you need to go back to the 1st concept to deal
with 64%5E2 (only working backwards)
64%5E2+=+%288%5E2%29%5E2
next
%288%5E2%29%5E2+=+8%5E%282%2A2%29
next
8%5E%282%2A2%29+=+8%5E4
---------------
%288%5E8%29%2A%28b%5E8%29+%2F+%2864%5E2%29%2A%28a%5E2%29
next
%288%5E8%29%2A%28b%5E8%29+%2F+%288%5E4%29%2A%28a%5E2%29
This is the same as:
%28%288%5E8%29%2F%288%5E4%29%29+%2A+%28%28b%5E8%29%2F+%28a%5E2%29%29
---------------
Another general concept:
a%5E5+%2F+a%5E3+=+a%5E%285-3%29
next
a%5E%285-3%29+=+a%5E2
---------------
%28%288%5E8%29%2F%288%5E4%29%29+%2A+%28%28b%5E8%29%2F+%28a%5E2%29%29
next
%288%5E4%29+%2A+%28%28b%5E8%29%2F+%28a%5E2%29%29
I'm not sure if this is exactly
what they want, but the method should be OK