Eli5: Why is 2^9 + 2^9 = 2^10

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Middle school teacher here, and this is driving me crazy! Thanks!

In: 2

This is because another way to write this is just 2 * 2^9. Just like 4 + 4 is 2*4. 2^9 is just 2 times itself 9 times. That means 2^10 is 2 times itself 10 times or 2 * 2^9 or 2^9 + 2^9.

Because every power of 2 is double the one before, and adding two numbers together is the same as doubling them.

Because its 2^n when going to the next n you just double the previous. So 2^10 is double 2^9. Same would be true for any one like that. 2^5 + 2^5 = 2^6

The difference between 2^9 and 2^10 is that 2^9 needs to be doubled one more time. Hence 2^9 + 2^9 = 2^10

When you do 2^9 + 2^9 it’s the same as 2 * 2^9 (as multiplication is just repeated addition) which is the same as 2^10 (as powers are just repeated multiplication)