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 ^{ yz } (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 }
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