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Q.1 Using laws of e×ponents, simplify and write the answer in e×ponential form:
(i) \(3^2 × 3^4 × 3^8\)
(ii)\( 6^{15} ÷ 6^{10}\)
(iii)\( a^3 × a^2\)
(iv)\( 7^x × 7^2\)
(v)\( (5^2)^3 ÷ 5^3\)
(vi) \(2^5 × 5^5\)
(vii) \(a^4 × b^4\)
(viii)\( (3^4)^3\)
(ix)\( (2^{20 }÷ 2^{15}) × 2^3\)
(x)\( 8^t ÷ 8^2\)
Answer :

(i) \(3^2 × 3^4 × 3^8 = 3^{2+4+8} = 3^{14} [a^m ÷ a^n = a^{m+n}]\)
(ii) \(6^{15} ÷ 6^{10} = 6^{15-10} = 6^5 [a^m ÷ a^n = a^{m-n}]\)
(iii) \(a^3 × a^2 = a^{3+2} = a^5 [a^m × a^n = a^{m+n}]\)
(iv)\( 7^x × 7^2 = 7^{x+2} [a^m × a^n = a^{m+n}]\)
(v)\( (5^2)^3 ÷ 5^3 = 5^{2×3} ÷ 5^3 = 5^6 ÷ 5^3 = 5^{6-3}\)
\(= 5^3 [(a^m)^n = a^{mn}, a^m ÷ a^n = a^{m-n}]\)
(vi) \( 2^5 × 5^5 = (2 × 5)^5 = 10^5 [a^m × b^m = (ab)^m] \)
(vii) \( a^4 × b^4 = (ab)^4 [a^m × b^m = (ab)^4] \)
(ix)\( (2^{20} ÷ 2^{15}) × 2^3 = 2^{20-15} × 2^3 =2^5 × 2^3 = 2^{5+3} = 2^8 \)
(x) \( 8^t ÷ 8^2 = 8^{t-2} \)