Made by :- Paritosh Malik Class :- 7 Section :- B Submitted to :- Mrs Annu Ma’am

Maths FA-2 Project

Powers & Exponents

Very large quantities like planetary masses and very small distances like atomic sizes are very

difficult to comprehend and compare without the use of exponents.

Examples :- 625=5*5*5*5=52

343=7*7*7=73

We can expand numbers by using factorization and write them as exponents with different bases :-729=3*3*3*3*3*3=36

72=2*2*2*3*3=23*32

2 4 2 * 2 * 2 * 2 16 3 3 * 3 * 3 * 3 81

Conversion into Power Notation

Laws of Exponents

The following laws of exponents are very useful to do operations of

multiplication and division in numbers involving exponents.

If (x) is a rational number and (a) and (b) are whole numbers then :- xa*xb=xa+b

Examples :- 33*34=(3*3*3)*(3*3*3*3)=37

We can get the same result using the law given: 33*34=33+4=37

Law : 1

If (x) is a rational number and (a) and (b) are the any whole ,then :- xa/xb = xa-b

27/23 = 2*2*2*2*2*2*2 = 24

2*2*2We can get the same result using the law given above :- 27/23 = 27-3 = 24

Law : 2

If (x) is a rational number and (a) and (b) are whole numbers ,then :- (xa)b = xab

(32)4 = 32* 32* 32* 32 = 32+2+2+2 = 38

We can get the same result using the law given above :- (32)4 = 32*4 = 38

Law : 3

If (x) is rational number other than zero ,then x0=1. x3/x3 = x3-3 = x0 (Using Law 2) andx3 / x3 = x*x*x = 1 or x0 = 1 x*x*x Thus we arrive at the law given above.

Law : 4

If (a) and (b) are rational numbers and (m) is any whole number ,then :- am * bm =(ab)m

32 * 42 = 3*3*4*4 = (3*4)*(3*4) = (3*4)2 = 122

Law : 5

If (a) and (b) are rational numbers and (m) is any whole number ,then :- am a m

bm b

32 / 32 = 32 = 3*3 = 3 3 = 3 2

52 = 5*5 = 5 5 5

Law : 6

=

This notation is very helpful to express very large numbers or very small numbers.

Any number can be expressed in scientific notation in the form (k)*10n where (k) is equal to one or more than one but less than ten and n is an integer.

Scientific Notation

The distance between the Earth and the Moon is about 370,000 km. If we have to express this in scientific notation.Step 1 :- Convert the large number into a decimal number, where the decimal is placed after the firs non-zero digit.

Example of Scientific Notation

3 7 0 0 0 0 370000 km = 3.70000 * 100000 km