Engineering ToolBox - Resources, Tools and Basic Information for Engineering and Design of Technical Applications!

# Laws of Indices

## Simplifying calculations by involving indices.

Multiplying two or numbers with the same base

xy xz = xy+z                       (1)

Dividing numbers with the same base

xy / xz = xy-z                     (2)

Raising power

(xy)z = xy z                    (3)

Number with index 0

x0 = 1                        (4)

Number raised with negative number

x-y = 1 / xy                     (5)

1 / x-y = xy                    (5b)

Number raised with a fractional number

xy/z = (xy)1/z                     (6)

32 34 = 36

(32)4 = 34 = 38

## 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.

## Engineering ToolBox - SketchUp Extension - Online 3D modeling!

Add standard and customized parametric components - like flange beams, lumbers, piping, stairs and more - to your Sketchup model with the Engineering ToolBox - SketchUp Extension - enabled for use with older versions of the amazing SketchUp Make and the newer "up to date" SketchUp Pro . Add the Engineering ToolBox extension to your SketchUp Make/Pro from the Extension Warehouse !

We don't collect information from our users. More about

## Citation

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

Modify the access date according your visit.

9.19.12