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Understanding Exponent Properties and Scientific Notation

This guide covers the fundamental properties of exponents, including product, power of a power, power of a product, negative exponents, zero exponents, and quotient of powers. You'll find clear explanations and examples illustrating how to apply these properties, such as simplifying expressions and converting numbers to scientific notation. Real-world applications and problems are included to enhance comprehension and foster practical skills in dealing with exponents.

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Understanding Exponent Properties and Scientific Notation

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  1. Using Properties of Exponents

  2. Properties of Exponentsa&b are real numbers, m&n are integers • Product Property: am * an=am+n • Power of a Power Property: (am)n=amn • Power of a Product Property: (ab)m=ambm • Negative Exponent Property: a-m= ; a≠0 • Zero Exponent Property: a0=1; a≠0 • Quotient of Powers: am= am-n;a≠0 an • Power of Quotient: b≠0

  3. Example 1 – Product Property • (-5)4 * (-5)5 = • (-5)4+5 = • (-5)9 = • -1953125

  4. Example 2 • x5 * x2 = • x5+2 = • x7

  5. Example 3 – Power of a Power • (23)4 = • 23*4 = • 212 = • 4096

  6. Example 4 • (34)2 = • 34*2 = • 38 = • 6561

  7. Example 5 – Neg. Exponent • (-5)-6(-5)4 = • (-5)-6+4 = • (-5)-2 =

  8. Example 6 – Quotient of Powers

  9. Example 7 – Power of Quotient

  10. Example 8 – Zero Exponent • (7b-3)2 b5 b = • 72 b-3*2 b5 b = • 49 b-6+5+1 = • 49b0 = • 49

  11. Example 9 – Quotient of Powers

  12. Scientific Notation • 131,400,000,000= 1.314 x 1011 Put that number here! Move the decimal behind the 1st number How many places did you have to move the decimal?

  13. 131,400,000,000 = 5,284,000 1.314 x 1011= 5.284 x 106 Example – Scientific Notation

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