Of the following expressions, which is equivalent to 2^x * 4^2x?

Rationale

2^x * 4^2x is equivalent to 25x.

To simplify the expression, we can rewrite 4 as 2^2, which allows us to express everything in terms of base 2: 4^(2x) becomes (2^2)^(2x) or 2^(4x). Thus, 2^x * 2^(4x) combines to 2^(x + 4x) = 2^(5x), which is the same as 25x.

A (25x) CORRECT

This choice correctly represents the simplified expression. By combining the exponents, we find that 2^x * 4^2x simplifies to 2^(5x), which is equivalent to 25x, confirming this as the correct answer.

B (29x) YOUR ANSWER

This option incorrectly suggests that the expression simplifies to 2^(9x). The correct method shows that 2^x * 4^2x simplifies to 2^(5x), not 2^(9x), making this choice incorrect.

C (24x²) YOUR ANSWER

This choice implies a different exponent and incorrect manipulation of the base. The expression simplifies to 2^(5x), not 2^(4x²). Thus, this option does not accurately reflect the correct simplification.

D (25x²) YOUR ANSWER

This choice suggests that the exponent of the base 2 should be 2x instead of 5x. The correct simplification reveals that the exponent is indeed 5x, making this choice incorrect.

Conclusion

The expression 2^x * 4^2x simplifies to 2^(5x), which is correctly represented as 25x. The other options reflect misunderstandings in exponent manipulation or incorrect assumptions about the expression's structure. Understanding how to manipulate exponents is crucial for simplifying expressions effectively.

Of the following expressions, which is equivalent to 2^x * 4^2x?

2^x * 4^2x is equivalent to 25x.

Related Questions

Related Quizzes

How familiar were you with this question?

Report an Issue

Rate this Practice Test