Which of the following expressions is equivalent to (4x^3)(5x²)?

Rationale

20x^5 is equivalent to (4x^3)(5x²).

To find the equivalent expression, we multiply the coefficients (4 and 5) and then add the exponents of x (3 and 2). Thus, the product is 20x^(3+2) = 20x^5.

A (9x^5) YOUR ANSWER

This option incorrectly suggests that the coefficient of the product is 9. The correct coefficient is obtained by multiplying 4 and 5, which equals 20, not 9. The exponent of x is correctly summed as 5, but the coefficient is incorrect.

B (9x^6) YOUR ANSWER

This choice is incorrect for both the coefficient and the exponent. The coefficient is again wrongly calculated as 9, and the exponent of x is mistakenly given as 6 instead of the correct sum of 5 (3+2).

C (20x^5) CORRECT

This expression is accurate as it correctly combines the coefficients (4 * 5 = 20) and adds the exponents (3 + 2 = 5). Thus, this option represents the correct equivalent expression for (4x^3)(5x²).

D (20x^6) YOUR ANSWER

This choice has the correct coefficient of 20 but incorrectly states the exponent of x as 6. The exponent should be the sum of 3 and 2, which is 5, not 6.

E (20x⁹) YOUR ANSWER

Here, the coefficient is correct at 20, but the exponent is incorrectly stated as 9. The correct exponent is achieved by adding 3 and 2, resulting in 5, not 9.

Conclusion

The expression (4x^3)(5x²) simplifies to 20x^5 by multiplying the coefficients and adding the exponents of x. Choice C accurately reflects this calculation, while all other options either miscalculate the coefficients or the exponents. Understanding these operations is crucial for algebraic manipulation and ensuring the accuracy of expressions.