SOLUTION: I need some assistance please (4^-3) ^4

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Question 1014758: I need some assistance please
(4^-3) ^4
Found 3 solutions by josgarithmetic, josmiceli, MathTherapy:
Answer by josgarithmetic(39617) About Me  (Show Source):
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Hi,
I think you want to know the basics of how
to raise a power to a power.
------------------------
I'll show you a more simple example.
+%28+3%5E5%29%5E3+
This is the same as:
+%28+3%2A3%2A3%2A3%2A3+%29%2A%28+3%2A3%2A3%2A3%2A3+%29%2A%28+3%2A3%2A3%2A3%2A3+%29+
So, just get rid of the parentheses and you have:
+%283%5E5%29%5E3+=+3%5E15+
also:
+%28+3%5E3+%29%5E5+=+3%5E15+
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So, in general,
+%28+x%5Ea+%29%5Eb+=+x%5E%28+a%2Ab+%29+
----------------------
Your problem is:
+%28+4%5E%28-3%29+%29%5E4+
+x+=+4+
+a+=+-3+
+b+=+4+
-----------
+%28+4%5E%28-3%29+%29%5E4+=+4%5E%28-12+%29+ answer
--------------------------
Also, according to what I stated:
+%28+4%5E%28-3%29%29%5E4+=+%284%5E4%29%5E%28-3%29+
-----------------------
Writing this out the long way:
+%28%28+1%2F4+%29%2A%28+1%2F4+%29%2A%28+1%2F4+%29%29%5E4+=+%28+4%2A4%2A4%2A4+%29%5E%28-3%29+
+%28+1%2F64+%29%5E4+=+256%5E%28-3%29+
------------------------
For the right side:
+x%5E%28-a%29+=+1%2F%28+x%5Ea+%29+
+256%5E%28-3%29+-+1%2F256%5E3+ so,
+1%2F64%5E4+=+1%2F256%5E3+
+1%2F16777216+=+1%2F16777216+
and those should also be the same as my answer:
+4%5E%28-12%29+=+1%2F16777216+
Hope I didn't throw too much at you
exponents can be challenging

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

I need some assistance please
(4^-3) ^4
%284%5E%28-+3%29%29%5E4

4%5E%28-+12%29 ------- Applying %28a%5Eb%29%5Ec = a%5E%28bc%29

highlight%28highlight_green%28highlight%28%281%2F4%5E12%29%29%29%29 ---- Applying x%5E%28-+y%29 = 1%2F%28x%5Ey%29