Simplifying Rational Exponents
We can easily simplify rational exponents by simplifying them into their simplest form using radicals. This is explained by the example added below:
Example: Simplify (27)4/3
Solution:
274/3 = (3√{27})4…(i)
Or
274/3 = 3√(27)4…(ii)
Form eq. (i)
274/3 = (3√{27})4
274/3 = (3)4
274/3 = 81
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