### 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

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 n ⋅ a m = a n+m 23 ⋅ 24 = 23+4 = 128 a n ⋅ b n = (a ⋅ b) n 32 ⋅ 42 = (3⋅4)2 = 144 Quotient rules a n / a m = a n–m 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 = n√b 81/3 = 3√8 = 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