Question

All Rules of exponents with examples

Answer 1

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 × ... × 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

Product rules a n ⋅ a m = a n+m

a n ⋅ b n = (a ⋅ b) n

Quotient rules a n / a m = a n-m

a n / b n = (a / b) n

Power rules (bn)m = bn⋅m

bnm = b(nm)

m√(bn) = b n/m

b1/n = n√b

Negative exponents b-n = 1 / bn

Zero rules b0 = 1

0n = 0 , for n>0

One rules b1 = b

1n = 1

Minus one rule

Derivative rule (xn)' = n⋅x n-1

Integral rule ∫ xndx = xn+1/(n+1)+C