Final answer:
The expression (8a¹⁵ + 16a¹⁰ - 40a⁵) / 8a⁵ simplifies to a¹⁰ + 2a⁵ - 5 by dividing each term individually and simplifying the exponents and coefficients.
Step-by-step explanation:
To simplify the expression (8a¹⁵ + 16a¹⁰ - 40a⁵) / 8a⁵, we need to first divide each term in the numerator by the term in the denominator.
For the first term, 8a¹⁵ / 8a⁵, we subtract the exponents (15 - 5) leaving us a¹⁰.
For the second term, 16a¹⁰ / 8a⁵, we divide the coefficients (16 / 8 = 2) and subtract the exponents (10 - 5) yielding 2a⁵.
For the third term, -40a⁵ / 8a⁵, we divide the coefficients (-40 / 8 = -5) and the a terms cancel out since they have the same exponent, leaving -5.
Combining all these, we get the simplified expression a¹⁰ + 2a⁵ - 5, which corresponds to Option A.