Introduction we will be looking at indices or powers. Either name can be used, and both names mean the same thing. Basically, they are a shorthand way of writing multiplications of the same number. So, suppose we have               4 × 4 × 4   We write this as ‘4 to the power 3’ : 4^3      So 4 × 4 × 4 = 4^3 The number 3 is called the power or index. Note that the plural of index is indices. NOTE: An index, or power, is used to show that a quantity is repeatedly multiplied by itself. An index, or power, is used to show that a quantity is repeatedly multiplied by itself.

a × a × a × a × a Since there are five a’s multiplied together we write this as ‘a to the power 5’.               a^5 So a × a × a × a × a = a^5 . What if we had 2x 2 raised to the power 4 ? This means four factors of 2x 2 multiplied together, that is,           2x^2 × 2x^2 × 2x^2 × 2x^2 = 16x^8