Simplify the following rational expression. Use absolute value symbols when needed.
3 √216/1728

1/2

Step-by-step explanation:

Absolute value symbols are only needed in certain cases when finding the nth root of a number when n is even. For example, the 4th root of (-2) ^ 20 is |(-2) ^ 5| or 32. To find a cube root, work backwards. Find a number whose cube is the radicand.  

Notice that the radical expression is of the form n√b, where b is a real number and n is a positive integer. This expression can be written as an exponential equation of the form a^n = b, where a is also a real number.

Write 3 √216/1728  as an exponential equation of the form a^n = b

a^3 = 216/1728

Because n is odd, there is only one value of a that makes the equation true. In this case, a will be a fraction.  Determine the numerator of a. Find the number that, when cubed, is 216.

(6)^3 = 216

Now determine the denominator of a. Find the number that, when cubed, is 1728.

(12)^3 = 1728

Use the numerator and denominator found above to complete the equation a^3 = 216/1728. . Since n is odd, absolute value symbols are not necessary.

(6/12)^3 = 216/1728

Finally, simplify this value of a.

6/12 = 1/2

Therefore, 3 √216/1728 = 1/2