# 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

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

and its value is 279,936.

2) 5 x 5 x 5 x 5 = 5

In general, in a

This process of using ex-ponents is called "raising to a power", where the ex-ponent is the "power". The expression "5

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

In general we can say that , a

1) 7 x 7 x 7 x 7 x 7

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

3) b x b x b x a x a

= b

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

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

1) 9

3) 7

Up till now we have discussed positive ex-ponents.

1) 10

2) 10

3) 10

1) (-3)

2) (-3)

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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}= 625In 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 = 7293) 7

^{4}**Product form :**7 x 7 x 7 x 7 = 2401Up till now we have discussed positive ex-ponents.

**Negative exponents****a**^{-n}= 1/a^{n}**Examples :**1) 10

^{-1}= 1/102) 10

^{-2}= 1/10^{2}= 1/1003) 10

^{-3}= 1/10^{3}= 1/1000**(-a)**

-a

^{n}= a^{n}when 'n' is even-a

^{n}, when 'n' is odd.**Examples :**1) (-3)

^{4}= 3^{4}since 4 is an even number.2) (-3)

^{3}= -3^{3}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)

• Laws of Ex-ponents

• Rational-Ex-ponents

• Integral-Ex-ponents

• Scientific notation

• Solved examples on Scientific Notation

• Solved Examples (Ex-ponents)