5a³(a⁹-6x)+(2a⁴)³-10a³x

To simplify the expression 5a³(a⁹-6x)+(2a⁴)³-10a³x, let's break it down into smaller parts.

First, let's simplify the expression inside the parentheses, a⁹ - 6x:

5a³(a⁹ - 6x) + (2a⁴)³ - 10a³x

Next, let's simplify the exponent of a in the expression (2a⁴)³. Remember that when you raise a power to a power, you multiply the exponents:

(2a⁴)³ = 2³ × (a⁴)³ = 8a¹²

Now, substitute the simplified expression back into the original expression:

5a³(a⁹ - 6x) + 8a¹² - 10a³x

Next, distribute the 5a³ to each term inside the parentheses:

5a³ × a⁹ - 5a³ × 6x + 8a¹² - 10a³x

Now, simplify the expressions with like terms:

5a¹² - 30a⁴x + 8a¹² - 10a³x

Combine the like terms:

(5a¹² + 8a¹²) - 30a⁴x - 10a³x

Combine the coefficients of the like terms:

13a¹² - 30a⁴x - 10a³x

So, the simplified expression is 13a¹² - 30a⁴x - 10a³x.