Question

Using laws of exponents, simplify and write the answer in exponential form: 
(i) 32 × 34 × 38 (ii) 615 ÷ 610 (iii) a³ × a² (iv) 7x×7² (v) (5²) ÷ 5³ (vi) 2⁵ × 5⁵ (vii) a⁴ × b⁴ (viii) (34)³(ix) (220 ÷ 215)×23 (x) 8t ÷ 82

Answer 1

(i) 3² x 3⁴ x 3⁸ = (3)^{2 + 4 + 8} (a^m x aⁿ = a^m+n) = 3¹⁴

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(ii) 6¹⁵ ÷ 6¹⁰ = (6)¹⁵ - 10 (a ^m ÷ a ⁿ = a ^m-n ) = 65

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(iii) a ³ x a ² = a ^{(3 + 2)} (a ^m x a ⁿ = a ^m+n ) = a ⁵

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(iv) 7^x + 7² = 7^{x + 2} (a ^m x a ⁿ = a ^m+n ) 

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(v) 5⁽²⁾³ ÷ 5³ = 5^{2 x 3} ÷ 5³ (a^m)ⁿ = a^mn = 5⁶ ÷ 5³ = 5^{(6 - 3)} (a^m ÷ aⁿ = a^m-n) = 5³

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(vi) 2⁵ x 5⁵ = (2 x 5)⁵ [a^mxb^m = (a x b)^m ] = 10⁵

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(vii) a⁴xb⁴ = (ab)⁴ [a ^m x b ^m = (a x b) ^m ]

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(viii) (3⁴) ³ = 3^{4 x 3} = 3¹² (a ^m ) ⁿ = a ^mn 

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(ix) (2²⁰ ÷ 2¹⁵) x 2³ = (2^{20 - 15}) x 2³ (a^m ÷ aⁿ = a^m-n) = 2⁵ x 2³ = (2⁵ + 3) (a^m x aⁿ = a^m+n) = 2⁸

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(x) 8^t ÷ 8² = 8^{(t - 2)} (a ^m ÷ a ⁿ = a ^m-n )