List 3 different ways to write 8 20 as the sum of 2 powers of 2?
To find three different ways to write 8 20 as the sum of two powers of 2, you can follow these steps:
Step 1: Recognize the powers of 2
First, let's identify the powers of 2. The powers of 2 are numbers that can be obtained by repeatedly multiplying 2 by itself. They include: 2, 4, 8, 16, 32, and so on.
Step 2: Start with the largest power of 2
For one way to write 8 20 as the sum of two powers of 2, start with the largest power of 2 (which is 16) and subtract it from 8 20:
8 20 - 16 = 804.
Step 3: Find the complement
To complete the sum, find a power of 2 that, when added to 804, equals 8 20. In this case, 804 can be expressed as 2^2 * 201, so the complement would be 4 (2^2) since 201 is not a power of 2.
Therefore, 8 20 can be written as 2^4 + 2^2.
Step 4: Repeat steps 2 and 3
To find two additional ways to write 8 20 as the sum of two powers of 2, repeat steps 2 and 3, excluding the powers of 2 that have already been used.
Second way:
8 20 - 8 = 8 12
8 12 can be expressed as 2^3 * 203, so the complement would be 2 (2^1) since 203 is not a power of 2.
Therefore, 8 20 can also be written as 2^3 + 2^1.
Third way:
8 20 - 4 = 8 16
8 16 can be expressed as 2^4 * 203, so the complement would be 0 since 203 is not a power of 2.
Therefore, 8 20 can also be written as 2^4 + 0.
In summary, three different ways to write 8 20 as the sum of two powers of 2 are:
1) 8 20 = 2^4 + 2^2
2) 8 20 = 2^3 + 2^1
3) 8 20 = 2^4 + 0