1. . Class –vii Chapter – 13 Contents Introduction Exponent Laws of exponent

2. INTRODUCTION The mass of the earth is 5,970,000,000,000,000,000.kg. The mass of the Uranus is 86,800,000,000,000,000,000,000,000.kg. These very large numbers are difficult to read and understand.To make the numbers easy to read and understand, we use exponent.

3. What is exponent? A large number 10000 can be written as 10 x 10 x10 x 10 = 10 4 10 4 is the shortest form of 10,000 this form is called exponent. The number 10 4 is read as 10 raised to the power 4. Base –10,Exponent - 4

4. Exponent form of the number Express the following numbers in exponent form- (a) 256 (b) 2025 (c) 432 256 =2 x 2 x 2 x 2 x2 x 2 x 2 x 2=2 8 2025 = 3 x3 x 3 x 3 x 5 x 5 = 3 4 x 5 2 432 = 2 x 2 x 2 x 2 x 3 x 3 x 3=2 4 x 3 3

5. LAWS OF EXPONENT Multiplying powers with same base (1) 2 4 x 2 3 = 2 x 2 x 2 x 2 x 2 x 2 x 2 =2 7 2 4 x 2 3 =2 4+3 = 2 7 (2) 5 3 x 5 2 = 5 x 5 x 5 x 5 x 5 = 5 5 5 3 x 5 2 = 5 3+2 = 5 5 (3) When the bases are same the powers are added. (4) For any non zero integer ‘a’ a m x a n = a m+n, where m, n are integer.

6. MULTIPLICATION OF TWO NUMBERS IN EXPONENT FORM Two numbers taken in exponent form can have Same Base Same base & exponent Same exponent 2 4 x 2 6 2 4 x 2 4 2 4 x 3 4 = 2 4+6 (2x3) 4 = 2 10 2 4+4 (2x2) 4 = 6 4 =2 8 = 4 4 Law 2 used : = 256 = 256 a m x b m = (a x b) m Law used: Law 2 Law 1 used is Law 1 a m x a n = a m+n

7. DIVISION OF TWO NUMBERS IN EXPONENT FORM Two numbers taken in exponent form Same base Same base & Same exponent Same exponent 5 4 ÷ 5 6 5 4 ÷ 5 4 2 4 ÷ 3 4 = 5 4 - 6 = (2 ÷ 3) 4 = 5 -2 = 5 4 - 4 (5 ÷5) 4 Law used: Law 1 used := 5 0 = 1= (5 4 ÷5 4 ) a m ÷ b m = (a ÷ b) m a m ÷ a n = a m-n Law 1 used := 1 a m ÷ a n = a m-n & Law used: a 0 = 1a m ÷ b m = (a ÷ b) m

8. NUMBERS WITH EXPONENT WITH ZERO Take two numbers in exponent form 3 5 ÷ 3 5. It can be simplified as: Without using law Using Law 3 5 ÷ 3 5 3 5 ÷ 3 5 = 3x3x3x3x3 = 3 5 - 5 3x3x3x3x3 = 3 0 = 1 = 1 This show that 3 0 = 1 Thus a 0 = 1 Note: 0 0 is not defined

9. Taking Power of a Power Take one number in exponent form and take its power example : (2 4 ) 3 = 2 4x3 = 2 12 Law used : (a m ) n =a mn

10. Using laws of exponents,simplify and write the answer in exponential form : (i) 3 2 x 3 6 (ii) 2 5 x 6 5 (iii) 6 15 ÷ 6 10 (iv) 2 5 ÷ 5 5 ( v) (3 4 ) 3 TRY THESE

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