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# 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

3234 = 36

(32)4 = 3 2  4 = 3 8

## Related Topics

• ### Mathematics

Mathematical rules and laws - numbers, areas, volumes, exponents, trigonometric functions and more.

## Related Documents

• ### Algebraic Expressions

Principal algebraic expressions formulas.
• ### Decimal System Prefixes

Prefix names used for multiples and submultiples units.
• ### Fractions

Law of fractions
• ### Logarithms

The rules of logarithms - log10 and loge for numbers ranging 1 to 1000.
• ### Oblique Triangle

Calculate oblique triangles.
• ### SI System

An introduction to the SI metric system.
• ### Trigonometric Functions

Sine, cosine and tangent - the natural trigonometric functions.

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## Citation

• The Engineering ToolBox (2011). Laws of Indices. [online] Available at: https://www.engineeringtoolbox.com/laws-indices-d_1800.html [Accessed Day Month Year].

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5.16.12

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