Final answer:
The given expression simplifies to 1x^2/9z^4 when using only positive integer exponents. This is achieved by first subtracting exponents with the same base inside the parenthesis and then squaring every term.
Step-by-step explanation:
The goal of simplifying this expression is to break it down from its complex form to something more easily understood.
The expression given is ((-4x^(5)y^(2)z^(5))/(12x^(4)y^(2)z^(3)))^(2). We start by simplifying inside the parenthesis. This involves subtracting the exponents as the bases are the same for both x, y, and z: -4/12 simplifies to -1/3, x^(5-4) becomes x, y^(2-2) becomes 1, and z^(5-3) turns into z^2. So now, we have (-1/3x*z^2)^2.
Next, raise every term to the power of 2 (since the whole fraction is squared): (-1)^2 becomes 1, (1/3)^2 becomes 1/9, x^2 remains x^2, and (z^2)^2 becomes z^4. Therefore, after fully simplifying the given expression, we are left with 1x^2/9z^4.
Learn more about Simplifying Exponents