Final answer:
To solve the expression ((4x²)⁴×(−5x)³), we first raise the numerical coefficients and variables to their respective powers and then multiply the results. The final answer to the expression is −32,000x⁻¹¹, which corresponds to option A.
Step-by-step explanation:
To solve the expression ((4x²)⁴×(−5x)³), we need to apply the power to both the coefficients and the variables inside the parentheses. The power outside the parentheses affects everything inside, meaning we multiply the exponents of the variables and raise the numerical coefficients to the power indicated.
First, we calculate (4x²)⁴:
- 4⁴ = 256,
- (x²)⁴ = x⁸ (because 2×4 = 8).
Now, we calculate (−5x)³:
Next, we multiply the results:
- 256 x (−125) = −32,000,
- x⁸ x x³ = x⁻¹¹ (because we add the exponents: 8 + 3 = 11).
Combining them, we get −32,000x⁻¹¹, which matches option A. Therefore, the correct answer is A. −2560x⁻¹¹.