Question

How do you simplify (1/8)^(4/3) ?

Answer 1

Explanation:

the numerator (top part) of a fractional exponent means "to the power of ...".

the denominator (bottom part) of a fractional exponent means "the ...th root".

so,

(1/8)^(4/3) means the cubic root of 1/8 to the power of 4.

these 2 operations can be done in any sequence.

it is the same if we first put 1/8 to the power of 4 and then get the cubic root, or if we first get the cubic root of 1/8 and then put that result to the power of 4.

to keep the numbers small, I prefer here to start with the cubic root :

cubic root (8) = 2, because 2³ = 8.

and so, cubic root (1/8) = 1/2

(1/2)⁴ = 1/16

that's it.

(1/8)^(4/3) = 1/16

Answer 2

1/16

Explanation:

Rational Exponents can be rewritten as Radicals:

`((1)/(8))^{(4)/(3)}=\sqrt[3]{(1)/(8)}^(4)`

Take the cube root of 1/8 = 1/2.

Raise (1/2) to the 4th power