Final answer:
Divide the numerical coefficients and subtract the corresponding variable exponents. The result after dividing 28u3z5 - 25u7z5 by -4u5z2 is -7z3/u2 + 6.25u2z3.
Step-by-step explanation:
To divide the expression 28u3z5 - 25u7z5 by -4u5z2, we need to apply the rules of exponents and arithmetic operations:
- First, we divide the numerical coefficients: 28 divided by -4 equals -7, and -25 divided by -4 equals 6.25 (or 25/4).
- Next, we subtract the exponents of u, for the term with u3 we have 3 minus 5, which is -2, and for the term with u7, we have 7 minus 5, which is 2.
- Finally, we subtract the exponents of z, for both terms, 5 minus 2, which is 3.
The simplified expression is -7u-2z3 + 6.25u2z3.
To make u-2 positive, we can write it in the denominator as 1/u2.
The final answer after simplifying is -7z3/u2 + 6.25u2z3.