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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		=	(Fractional index)

y ^1/4		=

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

Fractional Indices

The general rule for fractional indices is y^b/a = .

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.