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
-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.
Exponents
• Laws of Ex-ponents
• Rational-Ex-ponents
• Integral-Ex-ponents
• Scientific notation
• Solved examples on Scientific Notation
• Solved Examples (Ex-ponents)
7th grade math
8th grade math
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