Polynomials:

-5a3power (4a4power – 3a + 1)

To simplify the given polynomial expression, let's start by distributing -5a^3 to each term inside the parentheses:

-5a^3 * (4a^4 - 3a + 1)

Distributing -5a^3 to each term yields:

-20a^7 + 15a^4 - 5a^3

Therefore, the simplified polynomial expression is -20a^7 + 15a^4 - 5a^3.