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2.1 Using Properties of Exponents

2.1 Using Properties of Exponents. p. 89. Properties of Exponents a&b are real numbers, m&n are integers. Product Property : a m * a n =a m+n Power of a Power Property : (a m ) n =a mn Power of a Product Property : (ab) m =a m b m Negative Exponent Property : a -m = ; a ≠0

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2.1 Using Properties of Exponents

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  1. 2.1 Using Properties of Exponents p. 89

  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. –1 115 118 = b. 118 115 = 1331 = 113 Example 1 – Evaluate numerical expressions Power of a product property Power of a power property Simplify and evaluate power. Negative exponent property = 118–5 Quotient of powers property Simplify and evaluate power.

  4. 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?

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

  6. A swarm of locusts may contain as many as 85 million locusts per square kilometer and cover an area of 1200 square kilometers. About how many locusts are in such a swarm? Use scientific notation in real life SOLUTION Substitute values.

  7. ANSWER The number of locusts is about 1.02 1011, or about 102,000,000,000. Write in scientific notation. Use multiplication properties. Product of powers property Write 10.2 in scientific notation. Product of powers property

  8. You try… 2. (–8)(–8)3 SOLUTION (–8)(–8)3 = (–8)(–8)3 Product of a powers property = (–8)(–512) Multiply = 4096 Simplify

  9. 2 3 3. 9 2 3 23 = 93 9 8 = 729 You try… SOLUTION Power of a quotient property Simplify and evaluate power.

  10. 6 • 10 – 4 9 • 107 4. 2 3 6 9 6 9 6 •10 – 4 9 • 107 • 10 – 4 – 7 = You try… SOLUTION quotient of power property add power • 10 – 11 = • 10 – 11 = Negative exponent property 2 3 1011 = Negative exponent property

  11. = b–4 +6+7 = b9 r–2–3 ( r – 2 )–3 ( s3 )–3 = b. s3 r 6 = s–9 c. 16m4n –5 2n–5 Simplify expressions Product of powers property a. b–4b6b7 Power of a quotient property Power of a power property = r6s9 Negative exponent property Quotient of powers property = 8m4n – 5 – (–5) = 8m4n0= 8m4 Zero exponent property

  12. Betelgeuse is one of the stars found in the constellation Orion. Its radius is about 1500 times the radius of the sun. How many times as great as the sun’s volume is Betelgeuse’s volume? 4 π (1500r)3 Betelgeuse’s volume 3 = 4 Sun’s volume πr3 3 4 π 15003r3 3 = 4 πr3 3 Astronomy Let r represent the sun’s radius. Then 1500r represents Betelgeuse’s radius. The volume of a sphere is πr3. 4/3 Power of a product property

  13. = 150031 ANSWER Betelgeuse’s volume is about 3.4 billiontimes as great as the sun’s volume. = 15003r0 Quotient of powers property Zero exponent property = 3,375,000,000 Evaluate power.

  14. Simplify the expression. Tell which properties of exponents you used. 5. x–6x5 x3 SOLUTION x–6x5x3 = x–6x5 + 3 Power of a product property = x2 Simplify exponents.

  15. = 7z4 y2 Simplify the expression. Tell which properties of exponents you used. 6. (7y2z5)(y–4z–1) SOLUTION (7y2z5)(y–4z–1) = (7y2z5)(y–4z–1) Power of a product property = (7y2 – 4)(z5 +(–1)) Simplify = (7y–2)(z4) Negative exponent property

  16. s 3 2 s 3 2 7. t–4 t–4 s (3)2 = (t–4 )2 s6 = t–8 = s6t8 Simplify the expression. Tell which properties of exponents you used. SOLUTION Power of a product property Evaluate power. Negative exponent property

  17. x4y–2 3 8. x3y6 x4y–2 3 (x4)3 (y–2)3 x3y6 = (x3)3(y6)3 x12y–6 = x9y18 x3 = y24 Simplify the expression. Tell which properties of exponents you used. SOLUTION Power of a powers property Power of a powers property Power of a Quotient property = x3y–24 Negative exponent property

  18. Assignment p. 91, 3-21 every third problem, 24-40 even

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