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Understanding Exponents: Repeated Multiplication of a Number

This guide explores the concept of exponents, which denote how many times a base number is multiplied by itself. It defines essential terms such as 'base' and 'exponent,' explaining how to express repeated multiplication as a power. The document provides examples of evaluating powers and converting whole numbers into their exponential forms, showcasing the relationship between standard and exponential notation. Key laws of exponents are also introduced to facilitate understanding for students learning about this fundamental mathematical concept.

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Understanding Exponents: Repeated Multiplication of a Number

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  1. Notes #5 Exponents

  2. Vocabulary Powers- repeated multiplication of a number. Exponent-tells how many times to use the baseas a factor. Base- the number being multiplied in a power

  3. Repeated multiplication can also be written as a power, using a base and an exponent. The exponent tells how many times to use the baseas a factor. 4 2 Base Exponent Reading Math Read 24 as “the fourth power of 2” or “2 to the fourth power.”

  4. Additional Example 1: Evaluating Powers Find each value. A. 44 Use 4 as a factor 4 times. 44 = 4 · 4 · 4 · 4 = 256 B. 73 Use 7 as a factor 3 times. 73 = 7 · 7 · 7 = 343 C. 191 191 = 19 Use 19 as a factor 1 time.

  5. Any number to the zero power, except zero is equal to 1. 60 = 1 100 = 1 190 = 1 Zero to the zero power is undefined, meaning that it does not exist.

  6. To express a whole number as a power, write the number as a product of equal factors. Then write the product using the base and an exponent. Factor Form For example, 10,000 = 10 · 10 · 10 · 10 = 104. Standard Form to Exponential Form Standard Form Exponential Form

  7. Additional Example 2: Expressing Whole Numbers as Powers Write each number using an exponent and the given base. A. 625, base 5 5 is used as a factor 4 times. 625 = 5 · 5 · 5 · 5 = 54 B. 64, base 2 2 is used as a factor 6 times. 64 = 2 · 2 · 2 · 2 · 2 · 2 = 26

  8. Copy this table into your notes. Laws of Exponents

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