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.

Radicals

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:

 

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