Prove that: 1 1 + x a - b + 1 1 + x b - a = 1

We have to prove that 1 1 + x a - b + 1 1 + x b - a = 1 . Thus, we have, L H S = 1 1 + x a - b + 1 1 + x b - a = 1 1 + x a x b + 1 1 + x b x a [ ∵ a m a n = a m - n ] = 1 x b + x a x b + 1 x a + x b x a = x b x b + x a + x a x a + x b = x b + x a x b + x a = 1 = R H S . Therefore, we see that left hand side is equal to right hand side. Hence proved.

Simplify : a 2 n + 3 . a 2 n + 1 ( n + 2 ) a 3 2 n + 1 . a n 2 n + 1

Given, a 2 n + 3 . a 2 n + 1 ( n + 2 ) a 3 2 n + 1 . a n 2 n + 1 We know that if a is any non-zero integer and m and n are the whole numbers, then we have, a m n = a m n = a 2 n + 3 . a 2 n 2 + 5 n + 2 a 6 n + 3 . a 2 n 2 + n We know that, if a is any non-zero integer, and m and n are the whole numbers, then we have: a m × a n = a m + n = a 2 n + 3 + 2 n 2 + 5 n + 2 a 6 n + 3 + 2 n 2 + n We know that if a is any non-zero integer and m and n are the whole numbers, such that m > n ,then we have, a m ÷ a n = a m - n = a 2 n + 3 + 2 n 2 + 5 n + 2 - 6 n - 3 - 2 n 2 - n = a 2 Hence, the required answer is a 2

Simplify : x 2 n + 7 . x 2 3 n + 2 x 4 2 n + 3

Given, x 2 n + 7 . x 2 3 n + 2 x 4 2 n + 3 We know that if a is any non-zero integer and m and n are the whole numbers, then we have, a m n = a m n = x 2 n + 7 . x 6 n + 4 x 8 n + 12 We know that, if a is any non-zero integer, and m and n are the whole numbers, then we have: a m × a n = a m + n = x 2 n + 7 + 6 n + 4 x 8 n + 12 = x 8 n + 11 x 8 n + 12 = x 8 n . x 11 x 8 n . x 12 = 1 x Hence, the required answer is 1 x

E M B I B E

Concise Mathematics Middle School Class 8>Chapter 2 - Exponents (Powers)>EXERCISE 2(B)

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

Author:R K Bansal

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

Attempt the free practice questions on Chapter 2: Exponents (Powers), Exercise 2: EXERCISE 2(B) with hints and solutions to strengthen your understanding. Concise Mathematics Middle School Class 8 solutions are prepared by Experienced Embibe Experts.