Question 23

2^5x

The expression 2^x multiplied by 4^2x can be rewritten as 2^x multiplied by (2^2)^(2x), which simplifies to 2^x multiplied by 2^(4x). This results in 2^(x + 4x), which is 2^(5x).

A) 2^5x

This option is correct because it accurately represents the simplified form of the original expression. By combining the exponents of the base 2, we derive 2^(x + 4x) = 2^(5x), matching the expression provided.

B) 2⁹x

This option is incorrect as it suggests that the sum of the exponents results in 9x. The correct combination of the exponents is x + 4x, which equals 5x, not 9x.

C) 2^(4x²)

This option is also incorrect. It implies that the exponent is 4x², which does not correspond to any combination of x and 4x from the original expression. The exponent must be a linear combination, not a square.

D) 2^(5x²)

This option is incorrect as well because it suggests that the exponent is 5x². This does not align with the original expression, which results in a linear exponent, not a quadratic one.

Conclusion

The correct answer, 2^5x, is derived from properly simplifying the original expression through exponent addition. All other options fail because they either miscalculate the exponent or misinterpret the nature of the expression, leading to incorrect outcomes.