Exponents : Basic Rules

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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/aⁿ

Examples :

1) 10 ^-1 = 1/10

2) 10 ^-2 = 1/10 ² = 1/100

3) 10 ^-3 = 1/10 ³ = 1/1000

(-a)ⁿ = aⁿ when 'n' is even
-aⁿ, 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.

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Exponents

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

Number Sense
7th grade math
8th grade math
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