Simplify the expression: 15 x7 y6 3 x4 y3 a) 5 x4/7 y1/2 b) 5 x7/4 y2 c) 5 x10 y9 d) 5 x3 y3

Find the value of p for which the polynomial 3x^3 -x^2 + px +1 is exactly divisible by x-1, hence factorise the polynomial

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?

Acyclist bike x distance at 10 miles per hour .and returns over the same path at 8 miles per hour.what is the cyclist average rate for the round trip in miles per hour ?