An index, power or exponent is a way of shortening expressions such as 4 × 4 × 4 × 4 × 4 × 4 × 4 to 47

4p5 is a short way of writing 4 × p × p × p × p × p.

The 4 is called the coefficient , the p is called the base or variable and the 5 is called theindex, power or exponent.

Indices (plural of index) obey certain rules when they are being multiplied and divided.

Multiplication

When multiplying numbers or variables with indices, add the indices together.

The bases must be the same number or variable.

e.g a3 × a4 = a 3 + 4 = a7

because a3 × a4 = (a × a × a) × (a × a × a × a) = a7

 

Division

When dividing numbers or variables with indices, subtract the indices. The bases must be the same number or variable.

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