Question

Using laws of exponents, simplify and write the answer in exponential form:
(i) 2³ × 2⁴ × 2⁵
(ii) 5¹² ​÷ 5³
(iii) (7²)³
(iv) (3²)⁵ ​÷ 3⁴
(v) 3⁷ ​× 2⁷
(vi) (5²¹ ÷ 5¹³) × 5⁷

Answer 1

We have

(i) 2³ x 2⁴ x 2⁵ = 2^{(3 + 4 + 5)} = 2¹² [since a^m + aⁿ + a^p = a^(m+n+p)]

(ii) 5¹² ÷ 5³ = $\frac{5^{12}}{5^3}$ = 5^{12 - 3} = 5⁹ [ since a^m ÷ aⁿ = a^m-n ]
(iii) (7²)³ = 7⁶ [since (a^m)ⁿ = a^mn ]

(iv)(3²)⁵ ÷ 3⁴ = 3¹⁰ ÷ 3⁴ [since (a^m)ⁿ = a^mn ]
= 3^{(10 - 4)} = 3⁶ [since a^m ÷ aⁿ = a^m-n ]

(v) 3⁷ ​× 2⁷ = (3 x 2)⁷ = 6⁷ [since a^m x b^m = (a x b)^m ]

(vi) (5²¹ ÷ 5¹³) x 5⁷ = 5^{(21 -13)} x 5⁷ [since a^m ÷ aⁿ = a^m-n ]
= 5⁸ x 5⁷ [since a^m x bⁿ =a^{(m +n)}]
= 5⁽⁸⁺⁷⁾
= 5¹⁵