Exponents | Rules of Exponent

Exponents is important topic in algebra, Let’s understand exponents and each rule in detail, and see some examples.

What is an exponent

Exponents are the multiplication of the same thing by itself. An expression that represents repeated multiplication of the same factor is called a power.

Example: 43 = 4 X 4 X 4 = 64

Exponent

In words: 43 could be called “4 to the third power”, “4 to the power 3” or simply “4 cubed”
an = a × a × … × a
n times
a is the base and n is the exponent.

Rule name

Rule

Example

Product rules a na m = a n+m 23 ⋅ 24 = 23+4 = 128
a nb n = (a b) n 32 ⋅ 42 = (3⋅4)2 = 144
Quotient rules a n / a m = a nm 25 / 23 = 25-3 = 4
a n / b n = (a / b) n 43 / 23 = (4/2)3 = 8
Power rules (bn)m = bn⋅m (23)2 = 23⋅2 = 64
bnm
= b(nm)
232
= 2(32)= 512
m√(bn) =
b
n/m
2√(26) = 26/2 = 8
b1/n = nb 81/3 = 38 = 2
Negative exponents b-n = 1 / bn 2-3 = 1/23 = 0.125
Zero rules b0 = 1 50 = 1
0n = 0 , for n>0 05 = 0
One rules b1 = b 51 = 5
1n = 1 15 = 1
Minus one rule (-1)n = 1 , n is even
(-1)n = -1 , n is odd
(-1)5 = -1

I hope, this article will help you a lot to understand the Exponents | Rules of Exponent, in solving various problems related to this article, if you still have any doubts related to this article, you can ask it into the comment section. If you have any problem with any topic of mathematics you can post your problem in the comment section. You will get a reply shortly.

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