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 = 6^{7}

and its value is 279,936.

2) 5 x 5 x 5 x 5 = 5^{4}= 625

In general, in a^{n}, ‘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 "5^{3}" 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 "5^{3}" is commonly pronounced as "five cubed".
In general we can say that , a^{n} 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 : 7^{5} 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 : b^{3} x a^{2}

= b^{3}a^{2}

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) 9^{4}

Product form :9^{4} = 9 x 9 x 9 = 729

3) 7^{4}

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

Up till now we have discussed positive ex-ponents.

Negative exponents

a^{-n} = 1/a^{n}

Examples :

1) 10^{-1} = 1/10

2) 10^{-2} = 1/10^{2} = 1/100

3) 10^{-3} = 1/10^{3} = 1/1000

(-a)^{n} = a^{n} when 'n' is even
-a^{n}, when 'n' is odd.