EXPONENTS AND POWERS

TEAM: SUCCESS

INTRODUCTION

WHAT IS EXPONENTS ?

The exponent of a number says how many times to use that number in a multiplication.

It is written as a small number to the right and above the base number.

In this example: 82 = 8 × 8 = 64(The exponent "2" says to use the 8 two times in a multiplication.) Exponents are also called Powers or Indices

What if the Exponent is 1, or 0?

1 If the exponent is 1, then you just have the number itself (example 91 = 9)

0 If the exponent is 0, then you get 1 (example 90 = 1)Example: Powers of 5

   

52 1 × 5 × 5 25

51 1 × 5 5

50 1 1

5-1 1 ÷ 5 0.2

5-2 1 ÷ 5 ÷ 5 0.04

   

If you look at that table, you will see that positive, zero or negative exponents are really part of the same (fairly simple) pattern

LAWS OF EXPONENTS WITH EXAMPLES32 × 33 = 32 + 3 = 35 = 243

36/32 = 36 – 2 = 34 = 81

If a is any number except 0, then a0 = 1.

93/93 = 93 – 3 = 90 = 1

(22)3 = (2)2 × 3 = 2 6 = 64

(10)5 = (2 × 5)5 = 25 × 55

POWERS WITH NEGATIVE EXPONENTS

Negative ExponentsA NEGATIVE EXPONENT MEANS HOW MANY TIMES TO DIVIDE BY THE NUMBER.

Example: 8-1 = 1 ÷ 8 = 1/8 = 0.125Or many divides:

Example: 5-3 = 1 ÷ 5 ÷ 5 ÷ 5 = 0.008But that can be done an easier way:

5-3 could also be calculated like:1 ÷ (5 × 5 × 5) = 1/53 = 1/125 = 0.008

Use of exponents to express small no. in standard form

ANSWER THE FOLLOWING QUESTIONS :

Q 1. The value of 25 is _________ .(a)3 (b) 10 (c) 32 (d) 7

ans. c

In standard form 21600000 is written as • 2.16 × 107 (b) 216 × 107 (c) 2.16 × 105 (d) 216 × 100000

ans.a. Charge of an electron is 0.000,000,000,000,000,000,16 coulomb and in exponential form it can be written as• 16 × 10-18 coulomb (b) 1.6 × 10-21 coulomb (c) 1.6 × 10-19 coulomb (d) 16 × 10-21 coulomb

ans.c

MADE BY :GROUP:SUCCESSGROUPMEMBER: NIKITA,SALONI,VAIBHAV,VISHESH