Middle school teacher here, and this is driving me crazy! Thanks!
In: 2
A base is multiplied to itself using the exponent as a reference for that number of times it should be multiplied. So, it’s just repeated multiplication. Multiplication can be defined as repeated summation. And therefore, you can show from the bases of repeated multiplication, simplified down to the equivalent repeated addition of them, that the base 2 on each side of the equation is merely the repeated addition of itself the same number of times.
2^9 is 2 multiplied to itself 9 times and is equivalent to adding 256 “2’s” together. Since there are two terms, then on the left side are a combined 512 “2’s” added together. Or, 2*512.
2^10 is 2 multiplied to itself 10 times and is equivalent to adding 512 “2’s” together. Or, 2*512.
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