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

disclaimer: i'm not an expert.  i might be wrong...  this is just how i found the answer.

h=65

g=115

m=49

k=131

Step-by-step explaination:

Each side of the straight line has a measure of 180 degrees (if we ignore  the intersecting lines).

So, to find the measure of the angle below the given angles, we subtract the measured angles from 180 degrees.

180-115=65

180-131=49

The angles across from the given angles are the same, but in the reversed orders.  Hence,

h=65

g=115

m=49

k=131