13.1 Exponents

Exponents Exponents that are natural numbers are shorthand notation for repeating factors. 34 = 3 • 3 • 3 • 3 3 is the ________ 4 is the __________ (also called ________) Note by the order of operations that exponents are calculated before other operations.

The Product Rule Product Rule for Exponents If m and n are positive integers and a is a real number, then

Example Use the product rule to simplify. 32 · 34 z3 · z2 · z5 (3y2)(– 4y4)

Zero Exponent Zero Exponent If a does not equal 0, then a0 = ___. Example: Simplify each of the following expressions. 50 (xyz3)0 –x0

The Quotient Rule Quotient Rule for Exponents If a is a nonzero real number and m and n are integers, then

Example Use the quotient rule to simplify.

Negative Exponents Negative Exponents If a is a real number other than 0 and n is a positive integer, then

Example Simplify and write with positive exponents only.

Example Simplify and write with positive exponents only.