# Exponents : Basic Rules

In exponents we will mainly learn about ex-ponential form, product form, positive and negative powers and also about the scientific notation.Ex-ponents(power) are shorthand for repeated multiplication of the same thing by itself.

Example : 1) 6 x 6 x 6 x 6 x 6 x 6 x 6 , here there is a multiplication of 6 and 6 is repeated 7 times so this can be written in shortest way as 6 7 where 6 is the base and 7 is called ex-ponent.

So 6 x 6 x 6 x 6 x 6 x 6 x 6 = 67

and its value is 279,936.

2) 5 x 5 x 5 x 5 = 54= 625

In general, in an, ‘a ‘ is the base and ‘n’ is the exponent.
This process of using ex-ponents is called "raising to a power", where the ex-ponent is the "power". The expression "53" is pronounced as "five, raised to the third power" or "five to the third".

There are two specially-named powers: "to the second power" is generally pronounced as "squared", and "to the third power" is generally pronounced as "cubed". So "53" is commonly pronounced as "five cubed".
In general we can say that , an is called the nth power of a and can be read as :
a raised to the power n

Examples

1) 7 x 7 x 7 x 7 x 7

Ex-ponential form : 75 as 7 is repeated 5 times.

2)(3)x (-3) x (-3)

Ex-ponential form : (-3)3

3) b x b x b x a x a

Ex-ponential form : b3 x a2

= b3a2

4) (ab) x (ab) x (ab) x (ab)

Ex-ponential form : (ab)4

5) (4/3)x (4/3) x (4/3) x (4/3)

Ex-ponential form : (4/3)3

Examples of product form and its value :

1) 94

Product form :94 = 9 x 9 x 9 = 729

3) 74

Product form : 7 x 7 x 7 x 7 = 2401

Up till now we have discussed positive ex-ponents.

Negative exponents

a-n = 1/an

Examples :

1) 10-1 = 1/10

2) 10-2 = 1/102 = 1/100

3) 10-3 = 1/103 = 1/1000

(-a)n = an when 'n' is even
-an, when 'n' is odd.

Examples :

1) (-3)4 = 34 since 4 is an even number.

2) (-3)3 = -33 since 3 is an odd number.

Exponents

Laws of Ex-ponents
Rational-Ex-ponents
Integral-Ex-ponents
Scientific notation
Solved examples on Scientific Notation
Solved Examples (Ex-ponents)

Number Sense