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Study Guides > Intermediate Algebra

Introduction: Apply Exponent Rules

A common language is needed in order to communicate mathematical ideas clearly and efficiently. Exponential notation was developed to write repeated multiplication more efficiently. For example, growth occurs in living organisms by the division of cells. One type of cell divides 22 times in an hour. So in 1212 hours, the cell will divide 2222222222222\cdot{2}\cdot{2}\cdot{2}\cdot{2}\cdot{2}\cdot{2}\cdot{2}\cdot{2}\cdot{2}\cdot{2}\cdot{2} times. This can be written more efficiently as 2122^{12}. In this section we will learn how to simplify and perform mathematical operations such as multiplication and division on terms that have exponents. We will also learn how to use scientific notation to represent very large or very small numbers, and perform mathematical operations on them. The specific things you'll learn in this lesson include:
  • Simplify exponential expressions with like bases using the product, quotient, and power rules
  • Simplify exponential expressions with exponents of 00 and 11
  • Simplify compound expressions using the exponent rules

Learning activities for this lesson include:

  • Read: Terms and Expressions With Exponents
  • Self-Check: Terms and Expressions With Exponents
  • Read: Product and Quotient Rules
  • Self-Check: Product and Quotient Rules
  • Read: The Power Rule for Exponents
  • Self-Check: The Power Rule for Exponents
  • Read: Negative and Zero Exponent Rules
  • Self-Check: Negative and Zero Exponent Rules
  • Read: Find the Power of a Product and a Quotient
  • Self-Check:Find the Power of a Product and a Quotient