How do you simplify one over the cubed root of 2. The answer is the cubed root of 4 over 2. But how?

Answer 1

multiply the numerator and denomerator by the cube root of 4.

Answer 2

Problem: 1 / 2^ (1/3)

Solution: Make the denominator equal to a whole number and remembering to add exponents when multiplying LIKED terms with exponents, we can multiply the numerator and the denominator by 2 ^ (2/3). 2/3 is selected so 2/3 + 1/3 = 1, then

[ 1 / 2^ (1/3) ] x [ 2^ (2/3)/ 2^ (2/3) ] = [ 1 x 2^ (2/3) ] / [ 2^ (1/3) x 2^ (2/3) ]

= [ 1 x 2^ (2/3) ] / [ 2^ (1/3 +2/3) ]

= [ 2^ (2/3) ] / [ 2^ (1) ] = [ 2^ (2/3)] / [ 2 ] = 4^ (1/3) / 2 after

recognizing 2^ (2/3) is same as cube rt of 2^2 (see another ex below).

Find cube root of 8 in terms of exponents:

8 can be written as 2^3

therefore, cube root of 8 = [8]^ (1/3) = [2^3]^ (1/3) = cube root of (2^3)

Answer 3

1/cubed root of 2 = 1/(2^(1/3))

It's a standard practice to simplify fractions with roots in the denominator by moving the root to the top.

This is done by multiplying the bottom by something to make the exponent a 1. In this example it can be done by multiplying the top and bottom by the cubed root of 4... aka (2^2)^(1/3) ... aka 2^(2/3)

Multiply the top and bottom by the cubed root of four. Then the bottom becomes 2 because (2^(1/3))(2^(2/3)) = 2^1 because you can add the exponents 1/3+2/3 = 1.

Answer 4

1/cube(2) = cube(2) *cube(2)/cube(2) *cube(2) *cube(2) = cube(4)/2

cube(number)=cube root of number

Basically, you multiply both the top and the bottom of the fraction by the cube root of 2 squared (cube of 2 times the cube of 2). Since the cube root of 2, cubed is equal to 2, the bottom becomes 2. The cube root of 2 squared is equal to the cube root of 4:

cube(2) *cube(2) = cube(2*2) = cube(4)
cube(2) *cube(2) *cube(2) = cube(2*2*2) = cube(8) = 2

Answer 5

c(2) = cubic root of 2
1/c(2) = {c(2) * c(2)} / {c(2) * c(2) * c(2)} = c(4)/2.