SOLUTION: (125/8X to the 12 power ) all that raised to a -2/3 power. So 125 over 8X to the 12th power and all of that raised to the -2/3 power I tried 125 to the -2/3 over 8 to the -2/3 (ti

Question 72588: (125/8X to the 12 power ) all that raised to a -2/3 power. So 125 over 8X to the 12th power and all of that raised to the -2/3 power
I tried 125 to the -2/3 over 8 to the -2/3 (times) 8X to the -8 and got 125 over 8X to the -8.then fliped it because it is a negative exponent which would be 8X to the 8th over 125 which reduces to 2X to the 8th over 5? I really don't understand this at all.
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!

.
Sort of a complex problem. What can be done for openers is to recall that when you raise
a power to a power, you can just multiply the two exponents. So you can simplify the problem
by multiplying the (-2/3) exponent times the (+12) exponent to get a new single exponent of (-8).
The problem then becomes:
.

.
Next, to get rid of the negative exponent you can put the term with a positive exponent as
the denominator of a fraction whose numerator is 1. The problem then becomes:
.

.
Then by exponent rules the terms under the numerator can both be raised to the 8th power to get:
.

.
Next multiply the numerator and denominator of this fraction by .
The top
multiplies the and the bottom multiplies the .
.
This results in:
.

.
Notice the cancellation in the bottom:
.

.
So at this point we are at:
.

.
But by the rules of exponents the numerator can be expanded and the problem becomes:
.

.
Now, depending on how much further you want to go, you can divide by
and get (rounded off):
.
.
.
But maybe you could quit earlier than that or could use scientific notation to get
an answer of
.
Hope this helps you understand exponents a little more. A lot of practice with various rules
in doing this problem.
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