Of the following expressions, which is equivalent to 2^xÃ¢â€¹…4^2x?

Rationale

2^5x is equivalent to 2^x × 4^2x.

To simplify the expression 2^x × 4^2x, we can rewrite 4 as 2^2, leading to 4^2x being expressed as (2^2)^(2x) = 2^(4x). Thus, the expression becomes 2^x × 2^(4x) = 2^(x + 4x) = 2^(5x).

A (2^5x) CORRECT

This expression is correct as it directly results from the simplification of 2^x × 4^2x. The addition of exponents (x + 4x) gives us 5x, confirming that 2^5x is equivalent to the original expression.

B (2⁹x) YOUR ANSWER

This expression is incorrect because it suggests that the exponents have been added as 9x, which is not the case. The sum of exponents in the original expression correctly simplifies to 5x, not 9x.

C (2^(4x²)) YOUR ANSWER

This choice is incorrect as it implies that the exponent is 4x², which does not relate to the original expression. The simplification yields an exponent of 5x rather than a quadratic term like 4x².

D (2^(5x²)) YOUR ANSWER

This option is also incorrect because it presents a squared term in the exponent. The proper simplification yields an exponent of 5x, not a squared term, making this expression unrelated to the original.

Conclusion

The expression 2^x × 4^2x simplifies to 2^5x by combining exponents correctly. All other options incorrectly represent the exponentiation process or imply different exponents that do not match the original expression. Understanding exponent rules is crucial for accurate simplification in algebraic expressions.

Of the following expressions, which is equivalent to 2^xÃ¢â€¹…4^2x?

2^5x is equivalent to 2^x × 4^2x.

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