What is the result of (75 x 10 to the power of 3) + (25 x 10 to the power of 4)?

To solve the expression (75 x 10^3) + (25 x 10^4), it's important to note that both terms are expressed in scientific notation. However, to combine them directly, it's more efficient to express them with the same exponent.

First, rewrite the first term (75 x 10^3) in terms of 10^4:

• 75 x 10^3 can be rewritten as 7.5 x 10^4.

Now, the expression looks like this:

(7.5 x 10^4) + (25 x 10^4)

Next, since both terms now contain the same base of 10^4, they can be combined:

7.5 + 25 = 32.5.

So, we have:

32.5 x 10^4.

This representation is in proper scientific notation, as the coefficient (32.5) is between 1 and 10. The final result, therefore, is 32.5 x 10^4, which corresponds to the correct answer choice.

This reasoning demonstrates how changing the exponent to match allows for straightforward addition of the coefficients, leading to the correct final expression. The other choices either miscalculate the