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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.
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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
