Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Warm up 1) Evaluate 2) Evaluate 3) Evaluate 4) Evaluate 1 𝑞 𝑤ℎ𝑒𝑛 𝑞 = 4 3 2 𝑐 𝑤ℎ𝑒𝑛 𝑐 = 5 1 4 𝑑 𝑤ℎ𝑒𝑛 𝑑 = 2 3 6 𝑒 𝑤ℎ𝑒𝑛 𝑒 = 2 3 7.2 Apply Exponent Properties Involving Quotients • Notice what happens when you divide powers with the same base 𝑎5 𝑎 ∙ 𝑎 ∙ 𝑎 ∙ 𝑎 ∙ 𝑎 2 5−3 = = 𝑎 ∙ 𝑎 = 𝑎 = 𝑎 𝑎3 𝑎∙𝑎∙𝑎 Can you guess what the Rule is? Key Concept • Quotient of Powers Property • Let a be a nonzero real number and let m and n be positive integers such that 𝑚 > 𝑛 • WORDS: To divide powers having the same base subtract the exponents • Algebra: 𝑎𝑚 𝑎𝑛 • Example: 47 42 = 𝑎𝑚−𝑛 , 𝑎 ≠ 0 = 47−2 = 45 Example 1 Use the quotient of powers property a. 810 84 b. (−3)9 (−3)3 c. d. 54 ∙58 57 1 6 ∙ 𝑥 𝑥4 Power of a Quotient • Notice what happens when you raise a quotient to a power • 𝑎 4 𝑎 ( ) = 𝑏 𝑏 𝑎 𝑏 𝑎 𝑏 𝑎 𝑏 ∙ ∙ ∙ = 𝑎∙𝑎∙𝑎∙𝑎 𝑏∙𝑏∙𝑏∙𝑏 • Can you guess the rule? = 𝑎4 𝑏4 Key Concept • Power of a Quotient Property • Let a and b be real numbers with 𝑏 ≠ 0, and let m be a positive integer • Words To find a power of a quotient, find the power of the numerator and the power of the denominator and divide • • 𝑎 𝑚 𝑎𝑚 Algebra( ) = 𝑚 𝑏 𝑏 3 7 37 EX ( ) = 7 2 2 Example 2 Use the power of a quotient property a. b. 𝑥 3 ( ) 𝑦 7 2 (− ) 𝑥 Example 3 a. 4𝑥 2 3 ( ) 5𝑦 b. 𝑎2 5 ( ) 𝑏 Astronomy • The luminosity (in watts) of a star is the total amount of energy emitted from the star per unit of time. The order magnitude of the luminosity of the sun is 1026 𝑤𝑎𝑡𝑡𝑠. He star Canopus is one of the brightest stars in the sky. The order of magnitude of the luminosity of Canopus is 1030 watts. How many times more luminous is Canopus than the sun?