Cody

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.

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  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.

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  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)

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