Simplify, give the answer with positive index: - 2 2 × 0 3 × 3 3

Given, - 2 2 × 0 3 × 3 3 We know that, a m × b m = a × b m - 2 2 × 0 3 × 3 3 = - 2 × - 2 × 0 × 3 3 = 4 × 0 3 = 4 × 0 = 0 Hence, the required answer is 0 .

Simplify, give the answer with positive index: 4 x 2 y 3 3 ÷ 3 x 2 y 3 3

Given, 4 x 2 y 3 3 ÷ 3 x 2 y 3 3 We know that, ( a m ) n = a m n a m ÷ a n = ( a ) m - n a 0 = 1 4 x 2 y 3 3 ÷ 3 x 2 y 3 3 = 4 x 2 y 3 3 3 x 2 y 3 3 = 4 3 × x 6 × y 9 3 3 × x 6 × y 9 = 64 × x 6 × y 9 27 × x 6 × y 9 = 64 27 x 6 - 6 y 9 - 9 = 64 27 x 0 y 0 = 64 27 Hence, the required answer is 64 27 .

Simplify, give the answer with positive index: 1 2 x 3 × 6 x 2

Given, 1 2 x 3 × 6 x 2 We know that, a × b m = a m × b m a b m = a m b m a m a n = a m - n a - m = 1 a m 1 2 x 3 × 6 x 2 = 1 3 2 x 3 × 6 2 x 2 = 1 2 3 x 3 × 6 2 x 2 = 1 8 x 3 × 36 x 2 = 9 2 x 2 - 3 = 9 2 x - 1 = 9 2 x Hence, the required answer is 9 2 x .

Simplify, give the answer with positive index: 1 4 a b 2 c 2 ÷ 3 2 a 2 b c 2 4

Given, 1 4 a b 2 c 2 ÷ 3 2 a 2 b c 2 4 We know that, a b m = a m b m a m n = a m n x m ÷ x n = ( x ) m - n 1 4 a b 2 c 2 ÷ 3 2 a 2 b c 2 4 = 1 2 4 a b 2 c 2 ÷ 3 4 2 a 2 b c 2 4 = 1 4 2 a 2 b 4 c 2 ÷ 81 2 4 a 8 b 4 c 8 = 1 16 a 2 b 4 c 2 ÷ 81 16 a 8 b 4 c 8 = 1 16 a 2 b 4 c 2 × 16 a 8 b 4 c 8 81 = 1 81 × a 8 - 2 × b 4 - 4 × c 8 - 6 = a 6 c 6 81 Hence, the required answer is a 6 c 6 81 .

Simplify, give the answer with positive index: 5 x 7 3 . 10 x 2 2 2 x 6 7

Given, 5 x 7 3 . 10 x 2 2 2 x 6 7 We know that, ( a m ) n = a m n a m × a n = a m + n a m ÷ a n = ( a ) m - n a - m = 1 a m 5 x 7 3 . 10 x 2 2 2 x 6 7 = 5 3 × x 21 × 10 2 × x 4 2 7 x 42 = 125 × x 21 × 100 × x 4 128 x 42 = 12500 × x 21 + 4 128 x 42 = 12500 x 25 128 x 42 = 3125 32 x 25 - 42 = 3125 32 x - 17 = 3125 32 x 17 Hence, the required answer is 3125 32 x 17 .

Simplify, give the answer with positive index: 7 p 2 q 9 r 6 2 4 p q r 3 14 p 6 q 10 r 4 2

Given, 7 p 2 q 9 r 6 2 4 p q r 3 14 p 6 q 10 r 4 2 We know that, ( x m ) n = x m n x m × x n = x m + n x m ÷ x n = ( x ) m - n x - m = 1 x m 7 p 2 q 9 r 6 2 4 p q r 3 14 p 6 q 10 r 4 2 = 7 2 × p 4 × q 18 × r 12 × 4 3 × p 3 × q 3 × r 3 14 2 × p 12 × q 20 × r 8 = 49 × 64 × p 4 + 3 × q 18 + 3 × r 12 + 3 196 × p 12 × q 20 × r 8 = 3136 × p 7 × q 21 × r 15 196 × p 12 × q 20 × r 8 = 16 p 7 - 12 q 21 - 20 r 15 - 8 = 16 p - 5 q 1 r 7 = 16 q r 7 p 5 Hence, the required answer is 16 q r 7 p 5 .

E M B I B E

Concise Mathematics Middle School Class 7>Chapter 5 - Exponents>EXERCISE 5(B)

R K Bansal Solutions for Chapter: Exponents, Exercise 2: EXERCISE 5(B)

Author:R K Bansal

R K Bansal Mathematics Solutions for Exercise - R K Bansal Solutions for Chapter: Exponents, Exercise 2: EXERCISE 5(B)

Attempt the free practice questions on Chapter 5: Exponents, Exercise 2: EXERCISE 5(B) with hints and solutions to strengthen your understanding. Concise Mathematics Middle School Class 7 solutions are prepared by Experienced Embibe Experts.