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Algebra (Intermediate) - Indices
 
Indices | Fractional Indices | Rules for Indices
 
Indices

Indices are commonly referred to as ‘powers'.

For example, x3 is read as ‘x to the index 3' or ‘x to the power of 3'.

Indices tell us how many times the term is to be multiplied by itself.

For example: y3 = y x y x y

Other indices:
y-2
=
 1    
    y2   (Negative index)
         
y 1/3
 = cuberoot_y2     (Fractional index)
         
y 1/4
   = 4root_y2  

Note: The bottom number of the fraction gives the ‘root' of the term.

 

Fractional Indices
The general rule for fractional indices is yb/a =  broot_y2

 
Y0  = 1     (Zero index)
 
 
 

When the index is zero, the result is always 1.

 
Rules for Indices

Rule 1. When multiplying like terms, for example y3 x y5 = y8, we ADD the powers of y.

Again, 2y2 x 7y4 = 14 y6 (note, the 2 and the 7 are multiplied)


Rule 2. When dividing like terms, for example y8 / y2 = y6, we SUBTRACT the powers of y.

Again, 8y6 /4y2 = 2y4 (note, the 8 and the 4 are divided)


Rule 3. Brackets and indices, for example (y2) 4 = y8, the powers are multiplied in this case.