     #### Integer Exponents

A product of identical numbers is usually written in exponential notation. For example, 5 * 5 * 5 is written as 53 Exponential Notation:  #### Rules for Working with Exponents Simplifying Expressions with Exponents: Simplifying Expressions with Negative Exponents: #### Scientific Notation

Scientists use exponential notation as a compact way of writing very large numbers and very small numbers. For example, the nearest star beyond the sun, Proxima Centauri, is approximately 40,000,000,000,000 km away. The mass of a hydrogen atom is about 0.00000000000000000000000166 g. Such numbers are difficult to read and to write, so scientists usually express them in scientific notation. We know what 2n means whenever n is an integer. To give meaning to a power, such as 24/5, whose exponent is a rational number, we need to discuss radicals. The symbol √ means “the positive square root of.”  #### Rational Exponents

To define what is meant by a rational exponent or, equivalently, a fractional exponent such as a1/3, we need to use radicals.  Using the Laws of Exponents with Rational Exponents: Simplifying by Writing Radicals as Rational Exponents: Go back to  Real numbers    Go forward to  Algebraic Expression