What are all the powers if 4 that range from 4 through 1000

You're just going to take exponents of 4. For example, 4 to the power of 1, 4 to the power of 2, 4 to the power of 3, and so on. To get the powers of 4, just multiply 4 by how much the exponent reads. For example 4 to the power of 3 is just 4 multiplied by itself 3 times.

4^1=4

4^2=16

4^3=64

4^4=256

4^5=1024

However, 1024 is greater than 1000 so we do not include it.