The answers to these types of questions.

The area of a rectangle is 54x^9y^8 square yards. if the length of the rectangle is 6x^3y^4 yards, which expression represents the width of the rectangle in yards

1- is the product of two rational numbers irrational or rational? first, make a hypothesis by multiplying two rational numbers. then, use variables such as x=a/b and y=c/d and the closure property of integers to prove your hypothesis. 2- 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. 3- 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 part b?

Prove that the value of the expression 7^8–7^7+7^6 is divisible by 43.