Final answer:
The only expression equivalent to 25 * 2^x from the options provided is 25 * 2^x itself (option E). Other options change the base or the exponent in ways that are not equivalent to the original expression.
Step-by-step explanation:
The question asks which expressions are equivalent to 25 * 2^x. To find equivalent expressions, we need to understand how exponents and multiplication interact.
Starting with option F, (2^x)^5, we can use the rule of powers that states when we raise an exponent to another power, we multiply the exponents. In effect, this becomes 2^(5x). This is not equivalent because the base 2 is raised to a different power than in the original expression.
Now let’s consider option A, 25^x. This expression implies that 25 is the base, and it is raised to the power of x. In the original expression, 25 is not raised to a power, it is multiplied by 2 raised to the power of x, so this is not equivalent either.
Examining option E, 25 * 2^x, we see that it is simply the same as the original expression, making it equivalent.
After considering these examples, we can conclude that the equivalent expressions to 25 * 2^x from the given options are only 25 * 2^x itself.