Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Concept Notes/ Classes 7,8,9 Introducing Exponents In what follows, the expression βany numberβ for base means natural number or zero or integer or fraction or decimal or rational number or βotherβ numbers. 1 The First Definition of Exponents is as follows: If a is any number and k is any natural number other than 1 then the product a . a . a . a . ... k times is written as ππ and read as βa power kβ. 2 The Second Definition of Exponents is as follows: If a is any number, ππ is defined to be a. 3 The Third Definition of Exponents is as follows: If a is any number other than zero, ππ is defined to be 1. 4 The Fourth Definition of Exponents is as follows: If a is any number other than zero and k is any natural number then πβπ is defined to be the reciprocal of ππ . 5 The Fifth Definition of Exponents is as follows : π If a is any number and k is any natural number then ππ is the number which when multiplied by itself k times gives a, provided such number exists. 6 The Multiplication Rule of Exponents is as follows : If a is any positive number and x, y are any ______then product of ππ & ππ is ππ+π . 7 The Power Rule of Exponents is as follows : If a is any positive number and x, y are any ______________ then (ππ )π is πππ . 8 The Distributive Rule of Exponents is as follows: If a , b are any positive numbers and x is any ____________ then (ππ)π = ππ ππ . The Rules can be deduced from the definitions. These five definitions and three rules are also referred to as β the laws of exponentsβ. Why these Definitions are made and how these Rules are formed is a very interesting discussion! But it isadvisable to have this discussion after starting using these facts thoroughly.