What are Radicals and rational exponents?

Answer 1

A radical is a sort of reverse operation to raising a number to an integer power. So, for example, if y = x2 = x*x, then x is the principal square root of y. Similarly if y = x3 then x is the cube root of y. And so on for fourth root, fifth root, etc. There is the symbol √ . It is unicode character 214, but this browser will probably mess it up. It is preceded by a superscript 3, 4 ect to denote a cube root or a fourth root. A superscript 2 is implied rather than made explicit. Using the index (or power) laws, the square root of y can be written as y1/2, the cube root of y as y1/3, and so on.

A rational exponent is when the base number, b, is raised to a power which is a rational number. Thus b(p/q) is a rational exponent of b. Using the fact that p/q = p*(1/q) and the power laws,

b(p/q) = [bp](1/q) = q√(bp)

or b(p/q) = [b(1/q)]p = [q√(b)]p.

The second form is generally easier to use since it involves working with smaller numbers.