Final answer:
By dividing each term of the numerator by the denominator and simplifying further, the algebraic expression (-32v^5z^7 + 13v^2z^7) ÷ (-4v^4z^5) simplifies to 8vz^2 - 13/4 * z^2/v^2.
Step-by-step explanation:
We are given the algebraic expression (-32v^5z^7+13v^2z^7) divided by (-4v^4z^5) and we need to simplify it as much as possible. To simplify, we will first divide each term of the numerator by the denominator.
Step 1: Divide each term by the denominator:
-32v^5z^7 ÷ (-4v^4z^5) = 8v^(5-4)z^(7-5) = 8vz^2
13v^2z^7 ÷ (-4v^4z^5) = -13/4 * v^(2-4)z^(7-5) = -13/4v^-2z^2
Step 2: Simplify further by converting negative exponents into fractions:
-13/4v^-2z^2 = -13/4 * 1/v^2 * z^2 = -13/4 * z^2/v^2
Step 3: Combine the simplified terms:
8vz^2 - 13/4 * z^2/v^2
Now we have simplified the original expression to 8vz^2 - 13/4 * z^2/v^2. This is the most simplified form of the expression considering that the terms cannot be combined further due to different variables and exponents.
Step 4: Check the answer to see if it is reasonable.
Since we followed the proper rules of exponents and division, our simplification should be correct.