Using laws of exponents, simplify and write the answer in exponential

1.	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)3 ÷ 53(vi) 25 × 55(vii) a4 × b4(viii) (34)3(ix) (220 ÷ 215)(x) 8t ÷ 82
Answer» (i) 3² × 3⁴ × 3⁸ = 3^{2 + 4 + 8} = 3¹⁴ [∵ a^m × aⁿ = a^{m + n}] (ii) 6¹⁵ ÷ 6¹⁰ = 6^{15 – 10} = 6⁵ [∵ a^m ÷ aⁿ = a^{m – n}] (iii) a³ × a² = a^{3 + 2} = a⁵ [∵ a^m × aⁿ = a^{m + n}] (iv) 7^x × 7² = 7^{x + 2} [∵ a^m × aⁿ = a^{m + n}] (v) (5²)³ ÷ 5³ = 5^{2 × 3} ÷ 5³ = 5^{6 – 3} [(a^m)ⁿ = a^mn ∵ a^m ÷ aⁿ = a^{m – n}] (vi) 2⁵ × 5⁵ = (2 × 5)⁵ = 10⁵ [∵ a^m × b^m = (ab)^m] (vii) a⁴ × b⁴ = a⁴ × b⁴ = (ab)⁴ [∵ a^m × b^m = (ab)^m] (viii) (3⁴)³ = 3^{4 × 3} = 3¹² [(a^m)ⁿ = a^mn] (ix) (2²⁰ ÷ 2¹⁵) (2²⁰ ÷ 2¹⁵) × 2³ = 2^{20 – 15} × 2³ [a^m ÷ aⁿ = a^{m – n}] = 2⁵ × 2³ = 2^{5 + 3} = 2⁸ [a^m × aⁿ = a^{m + n}] (x) 8^t ÷ 8² = 8^{t – 2} [∵ a^m ÷ aⁿ = a^{m – n}]

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)3 ÷ 53(vi) 25 × 55(vii) a4 × b4(viii) (34)3(ix) (220 ÷ 215)(x) 8t ÷ 82

Answer»

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

(ii) 6¹⁵ ÷ 6¹⁰

= 6^{15 – 10} = 6⁵ [∵ a^m ÷ aⁿ = a^{m – n}]

(iii) a³ × a²

= a^{3 + 2} = a⁵ [∵ a^m × aⁿ = a^{m + n}]

(iv) 7^x × 7²

= 7^{x + 2} [∵ a^m × aⁿ = a^{m + n}]

(v) (5²)³ ÷ 5³

= 5^{2 × 3} ÷ 5³ = 5^{6 – 3} [(a^m)ⁿ = a^mn

∵ a^m ÷ aⁿ = a^{m – n}]

(vi) 2⁵ × 5⁵

= (2 × 5)⁵ = 10⁵ [∵ a^m × b^m = (ab)^m]

(vii) a⁴ × b⁴

= a⁴ × b⁴ = (ab)⁴ [∵ a^m × b^m = (ab)^m]

(viii) (3⁴)³

= 3^{4 × 3} = 3¹² [(a^m)ⁿ = a^mn]

(ix) (2²⁰ ÷ 2¹⁵)

(2²⁰ ÷ 2¹⁵) × 2³ = 2^{20 – 15} × 2³ [a^m ÷ aⁿ = a^{m – n}]

= 2⁵ × 2³

= 2^{5 + 3} = 2⁸ [a^m × aⁿ = a^{m + n}]

(x) 8^t ÷ 8²

= 8^{t – 2} [∵ a^m ÷ aⁿ = a^{m – n}]