Laws of Indices

Multiplying two or numbers with the same base

x^y x^z = x^{(y + z)}                (1)

Dividing numbers with the same base

x^y / x^z = x^{(y - z)}                  (2)

Raising power

(x^y)^z = x^{(y z)}                     (3)

Number with index 0

x⁰ = 1                        (4)

Number raised with negative number

x^-y = 1 / x^y                    (5)

1 / x^-y = x^y                  (5b)

Number raised with a fractional number

x^y/z = (x^y)^1/z                (6)

Examples

3²3⁴ = 3⁶ 

(3²)⁴ = 3^{(2  4)} = 3⁸