Question

Evaulate each expression:

(-1/8)^1/3

Would you make it 3 square root of -1/8? I don't know how to go from there.

(256/81)^1/4

Same thing, would it become 4 square root (256/81)?

Answer 1

(-1/8)^1/3
= (-1)^(1/3) / 8^(1/3)
= -1/2

check: (-1/2)(-1/2)(-1/2) = -1/8

(256/81)^(1/4) ---- the fourth root
= 4/3

exponents in fraction form are roots
1/3 is cube root
1/4 is fourth root, etc

if you have an exponent like 2/3,
look at it as 2(1/3)

so 8^(2/3)
could be (8^2)^(1/3) = 64^(1/3) = 4
or
(8^(1/3) )^2= 2^2 = 4