If a = - 1 2 and b = 1 3 , then find the value of 3 a 3 b 2 3

Given, a = - 1 2 , b = 1 3 Now, putting in ( 3 a 3 b 2 ) 3 , we get, 3 - 1 2 3 1 3 2 3 = 3 - 1 2 × - 1 2 × - 1 2 1 3 × 1 3 3 ⇒ 3 - 1 8 1 9 3 ⇒ 3 × - 1 8 × 1 9 3 = - 1 8 × 1 3 3 ⇒ - 1 24 3 = - 1 24 × - 1 24 × - 1 24 ⇒ - 1 13824 Hence, the required value is - 1 13824 .

If x y 2 = 7 9 5 ÷ 7 9 3 , then find y x 3

Given, x y 2 = 7 9 5 ÷ 7 9 3 Using the law, a m ÷ a n = a m - n , we get, ⇒ x y 2 = 7 9 5 - 3 ⇒ x y 2 = 7 9 2 When powers are same, then we can equate the base. Therefore, x y = 7 9 So, y x = 9 7 Thus, y x 3 = 9 7 3 ⇒ 729 343 Hence, the value of y x 3 is 729 343 .

If a = 3 and b = 4 , then find the value of 1 a + 1 b a + a b b

Given, a = 3 , b = 4 The value of 1 a + 1 b a + a b b after substituting the values of a and b , we get, ⇒ 1 a + 1 b a + a b b = 1 3 + 1 4 3 + 3 4 4 LCM of 3 , 4 = 12 ⇒ 4 + 3 12 3 + 3 4 4 = 7 12 3 + 3 4 4 ⇒ 7 12 × 7 12 × 7 12 + 3 4 × 3 4 × 3 4 × 3 4 ⇒ 343 1728 + 81 256 = 343 × 4 + 81 × 27 6912 ⇒ 1372 + 2187 6912 = 3559 6912 Hence, the required answer is 3559 6912 .

Evaluate: - 2 5 2 × 5 7 2 × 49 5 ÷ - 4 5 3 × 5 2 2 × 1 4

Given, - 2 5 2 × 5 7 2 × 49 5 ÷ - 4 5 3 × 5 2 2 × 1 4 - 2 5 2 × 5 7 2 × 49 5 ÷ - 4 5 3 × 5 2 2 × 1 4 = - 2 5 × - 2 5 × 5 7 × 5 7 × 49 5 ÷ - 4 5 × - 4 5 × - 4 5 × 5 2 × 5 2 × 1 4 ⇒ 4 25 × 25 49 × 49 5 ÷ - 64 125 × 25 4 × 1 4 ⇒ 4 25 × 25 49 × 49 5 ÷ - 64 125 × 25 4 × 1 4 ⇒ 4 25 × 25 49 × 49 5 ÷ - 4 5 × 1 1 × 1 1 ⇒ 4 5 ÷ - 4 5 4 5 × 5 - 4 = - 1 Hence, the required answer is - 1 .

E M B I B E

Maths Hub (ICSE)>Chapter 5 - Exponents and Powers>Brain Workout

S Purkayastha Solutions for Chapter: Exponents and Powers, Exercise 7: Brain Workout

Author:S Purkayastha

S Purkayastha Mathematics Solutions for Exercise - S Purkayastha Solutions for Chapter: Exponents and Powers, Exercise 7: Brain Workout

Attempt the free practice questions on Chapter 5: Exponents and Powers, Exercise 7: Brain Workout with hints and solutions to strengthen your understanding. Maths Hub (ICSE) solutions are prepared by Experienced Embibe Experts.