5. Of the following expressions, which is equivalent to 2^x * 4^2x?
Answer: A
2^x * 4^2x is equivalent to 25x.
The expression 2^x * 4^2x simplifies to 2^x * (2^2)^(2x), which further simplifies to 2^x * 2^(4x). Combining the exponents results in 2^(x + 4x) = 2^(5x), which can be expressed as 25x.
A) 25x
This option is correct because it reflects the simplified form of the original expression. The calculation shows that 2^x * 4^2x simplifies to 2^(5x), which is equivalent to 25x.
B) 29x
This option is incorrect. The expression 2^x * 4^2x does not simplify to this form because the exponents do not add up to 29x. The correct exponent addition leads to 5x, not 29x.
C) 24x²
This option is also incorrect. Simplifying 2^x * 4^2x does not yield a result with an exponent of 2 in the base of 2. The correct simplification shows 2^(5x), which indicates a linear relationship in x, not quadratic.
D) 25x²
This option is incorrect as well. The original expression does not result in an exponent of 2 for x. Instead, the simplification indicates that x is not squared, leading to 25x, not 25x².
Conclusion
The correct answer is 25x because it accurately represents the simplified form of the expression 2^x * 4^2x. All other options fail to reflect the correct exponent summation and do not match the mathematical simplification derived from the original expression.