SOLUTION: 4^square root of 2 * 4^2square root of 2 ive gotten this far: (2^2)^square root of 2 * (2^2)2square root of 2 i am supposed to simplify this expression but unfortunately my t

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: 4^square root of 2 * 4^2square root of 2 ive gotten this far: (2^2)^square root of 2 * (2^2)2square root of 2 i am supposed to simplify this expression but unfortunately my t      Log On


   

Question 253615: 4^square root of 2 * 4^2square root of 2
ive gotten this far: (2^2)^square root of 2 * (2^2)2square root of 2
i am supposed to simplify this expression but unfortunately my teacher ran out of time and we had little time to review this...any help would be greatly appreciated!
Found 2 solutions by jim_thompson5910, stanbon:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Is the problem 4%5E%28sqrt%282%29%29%2A4%5E%282%2Asqrt%282%29%29%5E%22%22 ??? If so, then...


4%5E%28sqrt%282%29%29%2A4%5E%282%2Asqrt%282%29%29%5E%22%22 Start with the given expression.


4%5E%28sqrt%282%29%2B2%2Asqrt%282%29%29%5E%22%22 Use the identity a%5Eb%2Aa%5Ec=a%5E%28b%2Bc%29


4%5E%28sqrt%282%29%281%2B2%29%29%5E%22%22 Factor out the GCF in the exponent.


4%5E%28sqrt%282%29%2A%283%29%29%5E%22%22 Combine like terms.


4%5E%283%2Asqrt%282%29%29%5E%22%22 Rearrange the terms.


So 4%5E%28sqrt%282%29%29%2A4%5E%282%2Asqrt%282%29%29=4%5E%283%2Asqrt%282%29%29%5E%22%22

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
4^square root of 2 * 4^2square root of 2
-----------------------------
4^(sqrt(2) * 4^(2sqrt(2))
---
= 4[sqrt(2) + 2sqrt(2)]
---
= 4[3sqrt(2)]
= 4^3 * 4^(sqrt(2))
---
= 64*4^(sqrt(2))
========================
Cheers,
Stan H.