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

Algebra ->  Radicals -> 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      Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!
%28%28125%2F%288%2AX%29%29%5E12%29%5E%28-2%2F3%29
.
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:
.
%28%28125%2F%288%2AX%29%29%5E%28-8%29%29
.
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:
.
1%2F%28%28125%29%2F%288%2AX%29%29%5E8%29
.
Then by exponent rules the terms under the numerator can both be raised to the 8th power to get:
.
1%2F%28%28125%5E8%29%2F%28%288%2AX%29%5E8%29%29
.
Next multiply the numerator and denominator of this fraction by %28%288%2AX%29%5E8%2F%288%2AX%29%5E8%29.
The top
%288%2AX%29%5E8 multiplies the 1 and the bottom %288%2AX%29%5E8 multiplies the %28%28125%5E8%29%2F%28%288%2AX%29%5E8%29%29.
.
This results in:
.
%288%2AX%29%5E8%2F%28%28%28125%5E8%29%2F%28%288%2AX%29%5E8%29%29%2A%288%2AX%29%5E8%29
.
Notice the cancellation in the bottom:
.

.
So at this point we are at:
.
%288%2AX%29%5E8%2F%28125%29%5E8
.
But by the rules of exponents the numerator can be expanded and the problem becomes:
.
%288%5E8%29%2A%28X%5E8%29%2F%28125%5E8%29
.
Now, depending on how much further you want to go, you can divide 8%5E8 by 125%5E8
and get (rounded off):
.
0.0000000003%2AX%5E8.
.
But maybe you could quit earlier than that or could use scientific notation to get
an answer of %282.814749767+%2A+10%5E%28-10%29%29%2AX%5E8
.
Hope this helps you understand exponents a little more. A lot of practice with various rules
in doing this problem.