6.1 Concept ByteProperties of Exponents

Chapter 6: Radical Functions & Rational Exponents

Simplifying Exponential Expressions

An algebraic expression is in simplest form when powers with a variable base are written with only positive exponents

Zero and Negative Exponents

For every nonzero number ,

For every nonzero number and integer ,

and

Example: Simplify each Expression

Multiplying Powers with the Same Base

To multiply powers with the same base, add the exponents

Example: Simplify each Expression

Raising a Power to a Power

To raise a power to a power, multiply the exponents

Raising a Product to a Power

To raise a product to a power, raise each factor to the power and multiply

Example: Simplify each Expression

Dividing Powers with the Same Base

To divide powers with the same base, subtract the exponents

Example: Simplify each Expression

Raising a Quotient to a Power

To raise a quotient to a power, raise the numerator and the denominator to the power and simplify

Example: Simplify each Expression