Which of the following expressions is equivalent to (4x²)(5x³)?

Rationale

20x⁵ is equivalent to (4x²)(5x³).

To simplify the expression (4x²)(5x³), we multiply the coefficients and add the exponents of the variable. This gives us 4 times 5 for the coefficients, which equals 20, and x raised to the power of (2 + 3), which equals x⁵. Thus, the final simplified expression is 20x⁵.

A (9x⁵) YOUR ANSWER

This choice incorrectly multiplies the coefficients and miscalculates the exponent. The coefficients of 4 and 5 yield 20, not 9, and the exponent should be 5, but the coefficient is incorrect.

B (9x⁶) YOUR ANSWER

Similar to choice A, this option also miscalculates the coefficients, arriving at 9 instead of the correct 20. Additionally, it incorrectly adds the exponents, resulting in 6 instead of the accurate total of 5.

C (20x⁵) CORRECT

This is the correct answer as it accurately multiplies the coefficients (4 * 5 = 20) and correctly adds the exponents (2 + 3 = 5), leading to the expression 20x⁵.

D (20x⁶) YOUR ANSWER

While this choice correctly multiplies the coefficients to arrive at 20, it incorrectly adds the exponents to get 6 instead of the correct sum of 5.

E (20x⁹) YOUR ANSWER

This option maintains the correct coefficient of 20 but incorrectly adds the exponents to reach 9, which is not the correct sum of the exponents in the expression.

Conclusion

The expression (4x²)(5x³) simplifies to 20x⁵ by correctly multiplying the coefficients and adding the exponents of the variable. All other choices either miscalculate the coefficients or incorrectly sum the exponents, confirming that 20x⁵ is the only valid equivalent expression.