Rational Exponents and Radicals
Rational exponets can easily be written as radicals. This is explained using the steps added below:
Take the rational exponent ap/q this can be changed to radical form as:
Step 1: Observe the given rational exponent, ap/q and now the numerator of the rational exponent is the power. In ap/q, p is the power.
Step 2: Again observe the given rational exponent, ap/q and now the denominator of the rational exponent is the root. In ap/q, q is the root.
Step 3: Write, base as the radicand, power raising to the radicand, and the root as the index. i.e.
ap/q = p√aq
This is explained by the example:
(3)2/3 = 3√(3)2
Rational Exponents
Rational exponents are those expressed as fractions or rational numbers that signify roots and fractional powers of any number. i.e. Rational exponents are numbers where the exponent parts are expressed as rational numbers, i.e. of the form ap/q. Rational exponents follow similar properties as integer exponents, including the product, quotient, and power rules. Rational exponents are used across various fields like physics, engineering and finance.
In this article, we will discuss the rational exponent’s definition, their formula, solved examples and others in detail.
Table of Content
- What are Rational Exponents?
- Properties of Rational Exponents
- Rational Exponents and Radicals
- Simplifying Rational Exponents
- Rational Exponents with Negative Bases
- Non-Integer Rational Exponents
- Applications of Rational Exponents