Calculate one-half to the seventh power times one-half to the second power all divided by one-half to the third power, giving your answer in its simplest form.
First, we need to simplify the numerator before dividing anything. Since we have like bases and we’re multiplying, we can go ahead and add our exponents. Seven plus two, which will simplify to be one-half to the ninth divided by one-half to the third. Now when you are dividing with like bases, you subtract your exponents.
So we have one-half to the nine minus three, which is one-half to the sixth power. So we should take one to the sixth power and two to the sixth power. One to the sixth power is one, and two to the sixth power is 64.
So our answer, in simplest form, would be one sixty-fourth.