Question

Write the following with rational, positive exponents.

a. sqrt of 8 = 8^1/2
b. seventh root of 5^2 = 5^2/7
c. sqrt sqrt 6 = ???
d. fourth root of sqrt of 5^3 = ???

Can someone please check my work and help with "c and d"? Thanks.

Answer 1

c. sqrt sqrt 6 = 6^1/4
d. fourth root of sqrt of 5^3 = (5^3)^1/8

Are these correct?
Note: for "d" do I just leave it like that or can I further simplify?

Thank you.

Answer 2

a. and b. are correct
c.
Recall that the (a^b)^c=a^(b*c)
sqrt(sqrt(x))=(x^(1/2))^(1/2)=x^(1/4)
d.
using again (a^b)^c=a^(b*c)
(sqrt(5^3)^(1/4))
=((5^3)^(1/2))^(1/4)
=((5^(3/2))^(1/4)
=5^((3/2)*(1/4))
=5^(3/8)