# Laws of Indices

## Simplifying calculations by involving 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

*x ^{0} = 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

*3 ^{2} 3^{4} = 3^{6} *

*(3 ^{2})^{4} = 3^{2 4 }= 3^{8}^{}*