Express 1000 using base 2 and exponents.

To express 1000 in base 2 and exponents, we first need to break down 1000 into powers of 2. This can be done by finding its binary representation.

First, find the largest power of 2 less than or equal to 1000.
2^9 = 512, which is the largest power of 2 less than 1000.
Subtract 512 from 1000: 1000 - 512 = 488.

Next, find the largest power of 2 less than or equal to 488.

2^8 = 256.
Subtract 256 from 488: 488 - 256 = 232.

Now, find the largest power of 2 less than or equal to 232.

2^7 = 128.
Subtract 128 from 232: 232 - 128 = 104.

Now, find the largest power of 2 less than or equal to 104.

2^6 = 64.
Subtract 64 from 104: 104 - 64 = 40.

Find the largest power of 2 less than or equal to 40.

2^5 = 32.
Subtract 32 from 40: 40 - 32 = 8.

Now, find the largest power of 2 less than or equal to 8.

2^3 = 8.
Subtract 8 from 8: 8 - 8 = 0.
So, we have the following powers of 2:

1000 = 2^9 + 2^8 + 2^7 + 2^6 + 2^5 + 2^3.

This is the expression of 1000 using base 2 and exponents.