2,500 can be expressed as which of the following powers of 10?

To express the number 2,500 as a power of 10, we begin by writing it in scientific notation. Scientific notation involves representing a number as a product of a number between 1 and 10, multiplied by a power of 10.

Starting with 2,500, we can rewrite it as 2.5 multiplied by a power of 10. To see how we arrive at this expression, we notice that moving the decimal point two places to the left gives us 2.5. Since we moved the decimal two places, we correspondingly increase the exponent of 10 by 2 to maintain the equality.

Thus, we have:

2,500 = 2.5 x 10^3

This indicates that we have shifted the decimal point to the left, which is effectively the same as multiplying 2.5 by 1,000 (10^3), yielding the original number of 2,500.

The reason this is the correct answer is that the scientific notation accurately reflects the value of 2,500 using one digit to the left of the decimal point and adjusting the exponent accordingly. The other options would not give us the correct representation of 2,500 when you convert them back from