Simplify and express in exponential form: 6 2 × 6 4 ÷ 6 3

To simplify 6 2 × 6 4 ÷ 6 3 and express it in exponential form. If a , b are integers and m , n are natural numbers, then a m × a n = a m + n a m a n = a m - n Now, 6 2 × 6 4 = 6 2 + 4 = 6 6 and 6 6 ÷ 6 3 = 6 6 - 3 = 6 3 Therefore, 6 2 × 6 4 ÷ 6 3 = 6 3

Simplify and express in exponential form: 2 2 3 × 3 6 × 5 6

To simplify 2 2 3 × 3 6 × 5 6 and express it in exponential form. If a , b are integers and m , n are natural numbers, then ab m = a m × b m a m n = a m n Now, 2 2 3 = 2 2 × 3 = 2 6 , 2 6 × 3 6 = 2 × 3 6 = 6 6 and 6 6 × 5 6 = 30 6 Therefore, 2 2 3 × 3 6 × 5 6 = 30 6

Simplify and express in exponential form: 8 2 ÷ 2 3

To simplify 8 2 ÷ 2 3 and express it in exponential form. If a , b are integers and m , n are natural numbers, then a m n = a m n a m ÷ a n = a m - n Now, 8 = 2 3 , 2 3 2 = 2 2 × 3 = 2 6 and 2 6 ÷ 2 3 = 2 6 - 3 = 2 3 Therefore, 8 2 ÷ 2 3 = 2 3

Simplify: 2 3 × a 3 × 5 a 4

To simplify 2 3 × a 3 × 5 a 4 and express it in exponential form. If a is an integer and m , n are natural numbers, then a m × a n = a m + n Now, 2 3 = 8 , a 3 × a 4 = a 3 + 4 = a 7 and 2 3 × a 3 × 5 a 4 = 8 × 5 × a 7 = 40 a 7 Therefore, 2 3 × a 3 × 5 a 4 = 40 a 7

Simplify: 2 × 3 4 × 2 5 9 × 4 2

To simplify 2 × 3 4 × 2 5 9 × 4 2 If a , b are integers and m , n are natural numbers, then a m × a n = a m + n a m a n = a m - n a × b m = a m × b m Now, 2 × 3 4 × 2 5 9 × 4 2 = 2 1 + 5 × 3 4 3 2 × 2 2 2 = 2 6 × 3 4 - 2 2 4 = 2 6 - 4 × 3 2 = 2 2 × 3 2 = 2 × 3 2 = 6 2 = 36 Therefore, 2 × 3 4 × 2 5 9 × 4 2 = 36

E M B I B E

Mathematics 7 Part II>Chapter 16 - Solved Examples>Exercise 1

Karnataka Board Solutions for Chapter: Solved Examples, Exercise 1: Exercise 1

Author:Karnataka Board

Karnataka Board Mathematics Solutions for Exercise - Karnataka Board Solutions for Chapter: Solved Examples, Exercise 1: Exercise 1

Attempt the free practice questions on Chapter 16: Solved Examples, Exercise 1: Exercise 1 with hints and solutions to strengthen your understanding. Mathematics 7 Part II solutions are prepared by Experienced Embibe Experts.