Express - 25 49 in the form of exponents.

Given rational number is - 25 49 , This can be written as, = - 5 × 5 7 × 7 = - 5 2 7 2 = - 5 7 2 ∴ a m b m = a b m Hence, - 25 49 = - 5 7 2 .

Express 27 125 in the form of exponents.

Given rational number is 27 125 , This can be written as, = 3 × 3 × 3 5 × 5 × 5 = 3 3 5 3 = 3 5 3 ∴ a m b m = a b m Hence, 27 125 = 3 5 3 .

Express 729 64 in the form of exponents.

Given rational number is 729 64 , This can be written as, = 3 × 3 × 3 × 3 × 3 × 3 2 × 2 × 2 × 2 × 2 × 2 = 3 6 2 6 = 3 2 6 ∴ a m b m = a b m Hence, 729 64 = 3 2 6 .

Prove 5 7 7 × 7 5 7 - 3 19 2 × 19 3 2 = 0 .

Let us consider L.H.S in the given expression. L.H.S = 5 7 7 × 7 5 7 - 3 19 2 × 19 3 2 = 5 7 7 7 × 7 7 5 7 - 3 2 19 2 × 19 2 3 2 Re-arranging the numerator and denominator, = 5 7 5 7 × 7 7 7 7 - 3 2 3 2 × 19 2 19 2 = 5 7 - 7 × 7 7 - 7 - 3 2 - 2 × 19 2 - 2 ∴ a m a n = a m - n = 5 0 × 7 0 - 3 0 × 19 0 = 1 × 1 - 1 × 1 = 1 - 1 = 0 L.H.S = R.H.S Hence, 5 7 7 × 7 5 7 - 3 19 2 × 19 3 2 = 0

Prove p q m × p q m × q p m = q p - m .

Let us consider L.H.S in the given expression. L.H.S p q m × p q m × q p m = p m q m × p m q m × q m p m Re-arranging the numerator and denominator, = p m q m × p m p m × q m q m = = p m q m × p m - m × q m - m ∴ a m a n = a m - n = p q m × p 0 × q 0 = p q m = q p - m ∴ a - m = 1 a m L.H.S = R.H.S Hence, p q m × p q m × q p m = q p - m

Prove 25 16 - 4 = 16 25 4 .

Let us consider L.H.S in the given expression. L.H.S = 25 16 - 4 = 25 - 4 16 - 4 ∴ a m b m = a b m = 5 × 5 - 4 4 × 4 - 4 = 5 2 - 4 4 2 - 4 = 5 - 4 × 2 4 - 4 × 2 ∴ a m n = a m × n = 5 - 8 4 - 8 = 4 8 5 8 ∴ a - m = 1 a m Now, R.H.S = 16 25 4 = 4 × 4 5 × 5 4 = 4 2 5 2 4 = 4 5 2 × 4 ∴ a m n = a m × n = 4 5 8 = 4 8 5 8 ∴ a m b m = a b m L.H.S = R.H.S Hence, 25 16 - 4 = 16 25 4

E M B I B E

Mathematics Class - VIII>Chapter 2 - Exponent>EXERCISE - 2.2

Chhattisgarh Board Solutions for Chapter: Exponent, Exercise 2: EXERCISE - 2.2

Author:Chhattisgarh Board

Chhattisgarh Board Mathematics Solutions for Exercise - Chhattisgarh Board Solutions for Chapter: Exponent, Exercise 2: EXERCISE - 2.2

Attempt the practice questions on Chapter 2: Exponent, Exercise 2: EXERCISE - 2.2 with hints and solutions to strengthen your understanding. Mathematics Class - VIII solutions are prepared by Experienced Embibe Experts.