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

3² 3⁴ = 3⁶

(3²)⁴ = 3^2 4 = 3⁸

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