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##.