Exponents indicate the number of times the number in front, is multiplied. As you can see, 2^2 means that the number 2 is multiplied 2 times, which yields 4.If we want to find what 2^3 is, we would simply take 2^2 and multiply it by 2. In other words we would be saying 2*2*2, which is 2^3, and that yields 8.
By multiplying 2, to each product, we can solve all the way up to 2^10, as indicated.
But how do we know what 2^0 and 2^1 are?
As you can see, we have multiplied each power of 2, by 2 to get the next power in the sequence. Dividing, is undoing a multiplication.
2^1:
So, if we know that: 
we can say that 
therefore, 2^1=2. We could also solve this by saying that 2 times itself just 1 time, is the same thing as 2*1, which is 2. Another way to look at it is to say that the exponent indicates how many times the number is being persented. Since the exponent is 1, that means that there is only 1 of the number 2.
we can say that 
therefore, 2^1=2. We could also solve this by saying that 2 times itself just 1 time, is the same thing as 2*1, which is 2. Another way to look at it is to say that the exponent indicates how many times the number is being persented. Since the exponent is 1, that means that there is only 1 of the number 2.2^0:
To solve 2^0, we can do the same thing. we can take 2^1 and divide backwards.
2 never does present itself in 2^0, and therefore 2 is shown 0 times. These last two strategies are not as helpful as the dividing backwards method. 
I like how you used many different patterns to show what the answer is to the power of 2's. This becomes very useful for students, and helps them learn the powers faster.
ReplyDeleteAnother awesome detailed lesson to help students with difficult problems. Powers can be confusing but the examples are great and easy to understand.
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