Let me try again, because I keep getting something different.
This is the problem:
( (2x^-4y-1)(2y^4z^-1) )^-2/2yx^3z^0
Can you please help me simply this. I didn't get what you got.
Thanks.
Ok, now that you have changed it again ....
but still have the denominator as ambiguous.
I will read it as
( (2x^-4y^-1)(2y^4z^-1) )^-2/(2yx^3z^0)
(4x^-4 y^3 z^-1)^-2 /(2y x^3)
= (1/16)(x^8 y^-6 z^2)/(2y x^3)
= (1/32)(x^5 y^-7 z^2
or
= x^5 z^2/(32y^7)
(2x^-4y^-1) = 2/(x^4 y)
(2y^4z^-1) = 2y^4/z
so, the numerator is
(2/(x^4 y) * 2y^4/z)^-2
= (4y^3 / x^4 z)^-2
= (x^8 z^2)/(16y^6)
Put all that over (2x^3 y) and you have
(x^5 z^2) / (32y^7)
We agree, Reiny, so it must be right!
nice, bob posted this question 3 times and each time there was a change in the way he typed it.
To simplify the expression in question, let's break down each part and apply the necessary operations.
1. Begin by simplifying the expressions within the parentheses.
Inside the first set of parentheses:
(2x^-4y-1) can be rewritten as (2/x^4y).
Inside the second set of parentheses:
(2y^4z^-1) can be rewritten as (2y^4/z).
2. Next, multiply the expressions within the second set of parentheses by -2.
-2 * (2y^4/z) = -4y^4/z.
3. Now, we need to simplify the denominator (2yx^3z^0) further.
z^0 equals 1, so the denominator simplifies to 2yx^3.
4. Finally, combine the numerator and denominator, and simplify the expression further.
(-4y^4/z) / (2yx^3) can be written as -4y^4 / (2y * z * x^3).
The 2 in the denominator cancels out with the 4 in the numerator, resulting in -2y^4 / (y * z * x^3).
Simplifying further, we have -2y^(4-1) / (z * x^3), which simplifies to -2y^3 / (z * x^3).
Therefore, the simplified form of the expression is -2y^3 / (z * x^3).