Addition and Subtraction of Powers (Exponents)

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Addition and Subtraction of Powers (Exponents)Rules for adding and subtracting exponents are 𝒂^(𝒑 + 𝒒)=𝒂^𝒑 × 𝒂^𝒒 𝒂^(𝒑 − 𝒒)=𝒂^𝒑/𝒂^𝒒 For Example 2^8=𝟐^(𝟓 + 𝟑)= 𝟐^𝟓 × 𝟐^𝟑 2^2=𝟐^(𝟓 − 𝟑)=𝟐^𝟓/𝟐^𝟑 We can try proving them Proof of Adding Exponents For 28 = 25 + 3 25 × 23 = (2 × 2 × 2 × 2 × 2) × (2 × 2 × 2) = 28 ∴ 25 × 23 = 25 + 3 = 28 For (−3)6 = (−3)4 + 2 (−3)4 × (−3)2 = (−3 × −3 × −3 × −3) × (−3 × −3) = −3 × −3 × −3 × −3 × −3 × −3 = (−3)6 ∴ (−3)4 × (−3)2 = (−3)4 + 2 = (−3)6 Proof of Subtracting Exponents For 22 = 25 – 3 2^5/2^3 = (2 × 2 × 2 × 2 × 2)/(2 × 2 × 2) = 2 × 2 = 2^2 ∴ 2^5/2^3 = 2^(5 − 3) = 2^2 For (−3)2 = (−3)4 – 2 (−3)^4/(−3)^2 = (−3 × −3 × −3 × −3)/(−3 × −3) = −3 × −3 = 〖(−3)〗^2 ∴ (−3)^4/(−3)^2 = 〖(−3)〗^(4 − 2)= 〖(−3)〗^2