Rewrite the rational exponent as a radical by extending the properties of integer exponents. 2 to the 7 over 8 power, all over 2 to the 1 over 4 power

Answer 1

This is a little confusing but I thing you are asking about simplifying this expression:

For numbers raised to a power that are the same base being divided, we subtract the exponents (and keep the base).

To subtract these fractions, we need a common denominator. That would be 8

7/8 - 2/8 = 5/8

So the answer becomes:

But the question is asking us to write the expression as a radical. The denominator of the fraction becomes the index to the radical and the numerator becomes the exponent for the base. So this becomes:

Then we can multiply 2 times itself 5 times (or plug 2⁵ into a calculator) to simplify it to 32 so the final answer would be: