Posted by **Math (URGENT)** on Sunday, May 2, 2010 at 5:21pm.

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.

- Math (URGENT) -
**Cody**, Sunday, May 2, 2010 at 5:42pm
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.

- Cody -
**MathMate**, Sunday, May 2, 2010 at 5:44pm
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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