When a number is written in expended from the exponents, each place is represent by a power of ____________.
When a number is written in expanded form with exponents, each place is represented by a power of 10.
To understand why, let's consider an example:
Let's take the number 536. In expanded form, it can be written as:
5 * 10^2 + 3 * 10^1 + 6 * 10^0
Here, each place value (hundreds, tens, ones) is represented by a power of 10. The base, which is 10 in this case, is raised to the power corresponding to the place value. The exponent tells you how many times to multiply the base (10) by itself.
So, in this example, 10^2 means multiplying 10 by itself twice, resulting in 100. Similarly, 10^1 means multiplying 10 by itself once, resulting in 10. Finally, 10^0 means multiplying 10 by itself zero times, resulting in 1.
Combining all the terms gives us the original number: 500 + 30 + 6 = 536.
Therefore, we can conclude that in expanded form with exponents, each place value is represented by a power of 10.