Sure, let's perform and simplify the division operation step by step.
First, we have two expressions, which is:
Numerator = 4v^(6)Z^(7) - 10v^(3)
Denominator = 2v^(4)Z^(2)
Now let's divide the numerator by the denominator.
Step 1: Divide the terms individually
We begin by dividing every term in the numerator by every term in the denominator, using the rule a^n / a^m = a^(n-m).
Dividing 4v^(6)Z^(7) by 2v^(4)Z^(2), we get:
2v^(6-4)Z^(7-2) = 2v^2*Z^5
Dividing -10v^(3) by 2v^(4)Z^(2) is not possible as the exponent of v in the denominator is greater than the exponent of v in the numerator. Hence, this term cannot be simplified any further and remains as it is, i.e., -10v^(3).
Step 2: Write down resultant division
Thus, the result of the division will consist of the first resultant term and a remainder:
Division result = 2v^2*Z^5
Remainder = -10v^3
Step 3: Report the simplified answer
On simplification, the complete result of the division operation between given expressions can be stated as the dividend along with the remainder. Therefore, the final simplified result is:
(2v^2*Z^5, -10v^3)
Here, the first term represents the result of the division while the second term is the remainder, which could not be divided by the denominator.
(4v^(6)Z^(7)-10v^(3))-:(2v^(4)Z^(2)) = (2v^2*Z^5, -10v^3)