Question

What are rational exponents, and how are they related to integer exponents?

Answer 1

See below

Explanation:

Integer exponents are a subset of rational exponents

Integer exponents

An integer exponent is an exponent that is an integer. For example, in the expression y = 5³, the 3 is an integer exponent.

An integer exponent is a power. Thus, 5³ = 5× 5× 5.

Rational exponents

Rational exponents can be expressed as a ratio of integers with nonzero denominators.

Thus, in the expression
`y = 5^{( 2)/(3 )}`, the fraction ⅔ is a rational exponent.

A rational exponent is both a power and an nth root. The numerator is the power, and the denominator is the root. Thus,

`5^{( 2)/( 3)} = \sqrt[3]{5^(2)} = (\sqrt[3]{5}})^(2)`