Integer Exponents and Scientific Notation

Negative Integer Exponents

Negative exponents represent the reciprocal of the base raised to the corresponding positive exponent.

• Definition: For any nonzero real number a and positive integer n,

• Example:

Review: Multiplying and Dividing Powers

When multiplying or dividing expressions with the same base, use the properties of exponents to simplify.

• Multiplication:

• Division: , where

• Power of a Power:

• Example:

  • Evaluate

Rules for Exponents (Product and Power)

These rules help simplify expressions involving exponents:

• Product Rule:

• Quotient Rule: ,

• Power Rule:

Example: Evaluate

• Step 1: Apply the negative exponent:

• Step 2: Apply the power to numerator and denominator:

• Step 3: Simplify exponents:

• Step 4: Calculate values: