SOLUTION: How would you work (4 to the 4th power)(over 8 to the 2nd power) to the 3rd power? I did this (4x4x4x4)(4x4x4x4)(4x4x4x4)over (8x8)(8x8) to the 3rd power

Algebra ->  Exponents -> SOLUTION: How would you work (4 to the 4th power)(over 8 to the 2nd power) to the 3rd power? I did this (4x4x4x4)(4x4x4x4)(4x4x4x4)over (8x8)(8x8) to the 3rd power      Log On


   

Question 483059: How would you work (4 to the 4th power)(over 8 to the 2nd power) to the 3rd power? I did this (4x4x4x4)(4x4x4x4)(4x4x4x4)over (8x8)(8x8) to the 3rd power
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
One way to do this is to notice that 4=2%5E2 and 8=2%5E3

So 4%5E4=%282%5E2%29%5E4=2%5E%282%2A4%29=2%5E8

and 8%5E2=%282%5E3%29%5E2=2%5E%283%2A2%29=2%5E6


In short, 4%5E4=2%5E8 and 8%5E2=2%5E6



So %28%284%5E4%29%2F%288%5E2%29%29%5E3=%28%282%5E8%29%2F%282%5E6%29%29%5E3


Now, let's simplify the inner expression %282%5E8%29%2F%282%5E6%29


%282%5E8%29%2F%282%5E6%29=2%5E%288-6%29=2%5E2


So this means that %28%284%5E4%29%2F%288%5E2%29%29%5E3=%282%5E2%29%5E3=2%5E%282%2A3%29=2%5E6=64


So in the end, %28%284%5E4%29%2F%288%5E2%29%29%5E3=64