# Laws Of Exponents

Exponents are also called Powers or Indices

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

In this example: 72 = 7 × 7 = 49

In words: 72 could be called "7 to the second power", "7 to the power 2" or simply "7 squared"

## b7

b7 = b × b × b × b × b × b × b = bbbbbbb

## What is an exponent?

The base a raised to the power of n is equal to the multiplication of a, n times:

a n = × a × ... × a

n times

a is the base and n is the exponent.

## Examples:

31 = 3

32 = 3 × 3 = 9

33 = 3 × 3 × 3 = 27

34 = 3 × 3 × 3 × 3 = 81

35 = 3 × 3 × 3 × 3 × 3 = 243

## Exponents rules and properties

 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)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