Understanding the Laws of Exponents: Multiplication and Division with Like Bases
This guide explores the fundamental concepts of multiplying and dividing powers with like bases. We demonstrate the multiplication of powers, showing that for any base 'a', ( a^m cdot a^n = a^{m+n} ). Similarly, for division, we illustrate that ( a^m / a^n = a^{m-n} ). Through various examples, we identify patterns in exponent operations, such as ( 8^3 cdot 8^2 = 8^5 ) and ( 4^5 / 4^2 = 4^3 ). By recognizing these patterns, learners can better grasp the properties of exponents applicable in algebra.
Understanding the Laws of Exponents: Multiplication and Division with Like Bases
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Presentation Transcript
Multiplying powers with like bases. 83∙ 82= • 8 ∙ 8 ∙ 8 ∙ • 8 ∙ 8 = 85 83∙ 82= 83+2 = 85 am ∙ an = am+n
Dividing powers with like bases. 45 • 4 ∙ 4 ∙ 4 ∙ 4 ∙ 4 = = 42 43 • 4 ∙ 4 ∙ 4 45 = 45+3 = 42 43 am = am-n an
Do you see a pattern? 24 = 16 23 = 8 22 = 4 21 = 2 20 = 2-1 = 2-2 = ÷ 2 ÷ 2 ÷ 2 ÷ 2 1 ÷ 2 ÷ 2
Do you see a pattern? 34 = 81 33 = 27 32 = 9 31 = 3 30 = 3-1 = 3-2 = ÷ 3 ÷ 3 ÷ 3 ÷ 3 1 ÷ 3 ÷ 3
Based on these patterns, we can conclude a0 = a-m = 34 = 81 33 = 27 32 = 9 31 = 3 30 = 3-1 = 3-2 = ÷ 3 1 ÷ 3 ÷ 3 ÷ 3 1 1 ÷ 3 am ÷ 3
