# 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 = 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)**

-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)