Question

Simplify the expression: (8a¹5 + 16a¹0 - 40a⁵) / 8a⁵.

A. a¹0 + 2a⁵ - 5
B. a¹0 + 4a⁵ - 10
C. a¹0 - 2a⁵ + 5
D. a¹0 - 4a⁵ + 10

Answer 1

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.