Question 36

20x^5

The expression (4x^3)(5x²) simplifies to 20x^5 when the coefficients and the powers of x are combined correctly.

A) 9x^5

Option A is incorrect because the product of the coefficients (4 and 5) is 20, not 9. Additionally, the powers of x are added correctly, resulting in x^(3+2) = x^5, but the coefficient is wrong.

B) 9x^6

Option B is incorrect as it presents both an incorrect coefficient and an incorrect exponent. The correct exponent is 5, derived from adding the powers of x, while the coefficient is 20, not 9.

C) 20x^5

Option C is correct. The multiplication of the coefficients (4 * 5) yields 20, and adding the exponents of x (3 + 2) gives x^5. Thus, this option accurately represents the expression.

D) 20x^6

Option D is incorrect because, while the coefficient of 20 is correct, the exponent of x is wrong. The correct exponent should be 5, not 6, as the powers of x must be added together.

E) 20x⁹

Option E is incorrect as it suggests an exponent of 9, which cannot be achieved through the addition of the powers of x in the original expression. The correct exponent remains 5.

Conclusion

The correct answer is 20x^5 as it accurately represents the product of the given expression by correctly calculating the product of the coefficients and the sum of the exponents. All other options fail to provide either the correct coefficient or the correct exponent, demonstrating a misunderstanding of the rules of exponents and multiplication.