Question 12

20x⁵

The expression (4x²)(5x³) simplifies to 20x⁵, as you multiply the coefficients and add the exponents of the variable x.

A) 9x⁵

This option is incorrect because while the exponent of x is accurate, the coefficient is not. The product of 4 and 5 is 20, not 9.

B) 9x⁶

This option is also incorrect. Although the exponent of x is incorrectly stated as 6, the coefficient remains incorrect as well, since 4 multiplied by 5 equals 20, not 9.

C) 20x⁵

This option is correct. When multiplying the coefficients 4 and 5, we obtain 20, and when adding the exponents of x (2 + 3), we get 5, resulting in the expression 20x⁵.

D) 20x⁶

This option is incorrect because, while the coefficient is correct at 20, the exponent of x is wrong. The correct exponent, obtained from the addition of 2 and 3, is 5, not 6.

E) 20x⁹

This option is incorrect as well. The coefficient is accurate at 20, but the exponent of x is incorrect. The correct exponent, derived from the addition of 2 and 3, is 5, not 9.

Conclusion

The correct answer, 20x⁵, is derived from correctly multiplying the coefficients and adding the exponents of the variable x. All other options either miscalculate the coefficient or misapply the laws of exponents, leading to incorrect results. This highlights the importance of proper arithmetic and exponent rules in algebraic expressions.