Find the area of the shaded region

The table shows a pattern of exponents. what is the pattern as the exponents decrease?

Find the constant of variation for the relation and use it to write an equation for the statement. then solve the equation.

1- what do you think the product of a nonzero rational number and an irrational number is? is it rational or irrational? make use of variables, the closure property of integers, and possibly a proof by contradiction to prove your hypothesis.2- why do we have to specify that the rational number must be nonzero when we determine what the product of a nonzero rational number and an irrational number is? if the rational number were 0, would it give us the same result we found in the first question?