Laws Of Exponents


Exponents are also called Powers or Indicaes

The exponent of a number says how many times to use the number in a multiplication.

In this example: 72 = 7 × 7 = 49

Exponents rules and properties

Rule name

Rule

Example

Product rules

a n x a m = a n+m

23 x 24 = 23+4 = 128

a n x b n = (a x b) n

32 x 42 = (3x4)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 = bnxm

(23)2 = 23x2 = 64

bnm = b(nm)

232 = 2(9)= 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)5 = -1

Derivative rule

(xn)' = n⋅x n-1

(x3)' = 3⋅x3-1

Integral rule

∫ xndx = xn+1/(n+1)+C

∫ x2dx = x2+1/(2+1)+C