SOLUTION: I don't understand how to simplify this question: (16 raised to the negative 1 power, "x" raised to the negative 4th power, "y" raised to the possitive 12th power) This whole pr

Question 95098: I don't understand how to simplify this question:
(16 raised to the negative 1 power, "x" raised to the negative 4th power, "y" raised to the possitive 12th power) This whole problem is in parenthesis. Outside of the parenthesis, the entire problem is raisd to negative 3/4.

I hope this makes sense.
So I think it should be written as:
(16^-1 x^-4 y^12)^-3/4

Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
Given:
.

.
By the power rule of exponents you multiply each of the exponents inside the parentheses
by the .
.
When you do that the problem becomes:
.

.
Note ... for some reason the 3 in the numerator of each multiplication gets clipped off.
Hope this doesn't confuse you.
.
Do the multiplication by in each of the exponents and you get:
.

.
At this point, let's just focus on . We can work the power rule in reverse and
get two different forms of this as follows:
.
Either or
.
Applying the power rule to either of these gets you back to .
.
So to evaluate this term we can either find the fourth root of 16 and cube it, or we can
cube 16 and take the fourth root of that answer. In this case it's easier to find the
fourth root of 16 which is 2 and cube that to get as the answer. So now we
can replace with and the problem is then down to:
.

.
But if a term in the numerator has a minus exponent, you can put that same term in the
denominator with a positive exponent. So we can change by putting it in the
denominator as and the answer to this problem becomes:
.

.
Notice that in taking the fourth root of x and y, to get real answers we must limit
both of these variables to positive values. Therefore, we need to make the answer have
positive values of x and y which we can do through absolute values. Therefore, the answer is:
.

.
Hope this helps you to understand the problem.
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