Final answer:
To simplify the expression (-40x^10 - 100x^11 + 10) / (10x^2), divide each term by 10x^2 and subtract the exponents to get a simplified expression of -4x^8 - 10x^9 + 1.
Step-by-step explanation:
To simplify the expression (-40x10 - 100x11 + 10) / (10x2) without negative exponents, we apply the rule of Division of Exponentials, which is to divide the digit term of the numerator by the digit term of the denominator and subtract the exponents of the exponential terms. Simplifying step-by-step:
- Divide each term in the numerator by 10x2.
- Simplify by subtracting the exponents where applicable (e.g., x10 divided by x2 becomes x10-2 or x8).
- Ensure all the exponents remain positive.
The simplified expression would be:
-4x8 - 10x9 + 1