# Exponents: Concepts & Formulas

Exponents: The base x raised to the power of p is equal to the multiplication of x, p times
xp = x ×x × ... × x( p times)
x is the base and p  is the exponent.
Examples
21 = 2
22 = 2 × 2 = 4
23 = 2 × 2 × 2 = 8
24 = 2 × 2 × 2 × 2 = 16, Here 2 is the base and 4 is the exponent.
Exponents rules and properties
 Rule name Rule Multiplication Rule xn⋅ xm=xm + n xn⋅yn= (x⋅y)n Division Rule xm/xn=xm-n xn/yn= (x/y)n Power Rule (xn)m=xn⋅m xnm= x(nm) m√(xn) =xn/m x1/n=n√x x-n= 1 /xn
• Exponents multiplication rules
Multiplication rule with same base
x n ⋅  x m = xm + n
Example:
23 ⋅ 25 = 23+5 = 28 = 2⋅2⋅2⋅2⋅2⋅2⋅2.2 = 256
Multiplication rule with same exponent
xn ⋅ yn = (x ⋅ y)n
Example: 32 ⋅ 22 = (3⋅2)2 = 36
• Exponent & Power division rules
Division rule with same base
xm / x n = xm-n
Example: 35 / 33 = 35-3 = 9
Division rule with same exponent
x n / y n = (x / y) n
Example: 93 / 33 = (9/3)3 = 27
• Exponents & powers rules
Power rule A
(xn) m =x nm
Example:
(23)2 = 232 = 26 = 2⋅2⋅2⋅2⋅2⋅2 = 64
Power rule B
Xnm = X(n)m
Example:
232 = 2(32) = 29 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 = 512
Power rule C
x1/n = n√x
Example:
271/3 = 3√27 = 3
Negative power rule
x-n = 1 / xn
Example:  2-2 = 1/22 = 0.25