Question

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

(i) 3² × 3⁴ × 3⁸ (ii) 6¹⁵ ÷ 6¹⁰ (iii) a³ × a²

(iv) 7^x× 7² (v) (vi) 2⁵ × 5⁵

(vii) a⁴ × b⁴ (viii) (3⁴)³

(ix) (x) 8^t ÷ 8²

Answer 1

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

= 3¹⁴

(ii) 6¹⁵ ÷ 6¹⁰ = (6)^{15 − 10} (a^m ÷ aⁿ = a^m−n)

= 6⁵

(iii) a³ × a² = a^{(3 + 2)} (a^m × aⁿ = a^m+n)

= a⁵

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

(v) (5²)³ ÷ 5³

= 5^{2 × 3} ÷ 5³ (a^m)ⁿ = a^mn

= 5⁶ ÷ 5³

= 5^{(6 − 3)} (a^m ÷ aⁿ = a^m−n)

= 5³

(vi) 2⁵ × 5⁵

= (2 × 5)⁵ [a^m × b^m = (a × b)^m]

= 10⁵

(vii) a⁴ × b⁴

= (ab)⁴ [a^m × b^m = (a × b)^m]

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

(ix) (2²⁰ ÷ 2¹⁵) × 2³

= (2^{20 − 15}) × 2³ (a^m ÷ aⁿ = a^m−n)

= 2⁵ × 2³

= (2^{5 + 3}) (a^m × aⁿ = a^m+n)

= 2⁸

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