What is half of 2 to the 6th power?

1 or 32

Your wording is unclear. Do you mean ##(1/2(2))^6## or ##1/2(2^6)##?
If you mean ##(1/2(2))^6##, then the answer is very simple. Half of two is one, and one to any power is still one.
Therefore your answer is 1.
If you meant ##1/2(2^6)##, then it is trickier. First, we must find ##2^6##.
This is just ##2 * 2 * 2 * 2 * 2 * 2## which is ##4 * 4 * 4##.
I’ve simply taken every pair of twos and multiplied them together.
Next, I multiply a pair of 4 together to get ##16 * 4##.
Finally, I multiply these together to get ##64##.
Now, we must multiply by a half, so ##64/2## is ##32##.

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