Question

Rewrite the expression with rational exponents as a radical expression by extending the properties of integer exponents.

two to the seven eighths power, all over two to the one fourth power

the eighth root of two to the fifth power
the fifth root of two to the eighth power
the square root of two to the five eighths power
the fourth root of two to the sixth power

Answer 1

I think it is the square root of two to the five eighths power but I'm not sure

Answer 2

you're on the right track - if you got 5/8 you probably did

2^(7/8) / 2^(1/4) = 2^(5/8)

however, this isn't a square root. looking at the exponent in 2^(5/8), the numerator becomes the new exponent and the denominator becomes the root

Answer 3

So is it the fifth root of two to the eighth power?

Answer 4

almost, remember the numerator is the new power ---> our numerator is 5 so it's 2 to the fifth power

denominator is 8 so this becomes the 8th root

the eighth root of two to the fifth power