INDICES

TIP: When doing these sort of problems, remember:

a) There are several rules of using indices which apply to specific numbers and general
    algebraic equations. You'll have to learn these, so here they are:

x^m  x  xⁿ = x^m+n        (example 2² x 2³ = 2⁵, which is 2x2 x 2x2x2)

x^m/xⁿ = x^m-n            (example 2²/2³ = 2^-1, which from the other rule below = ½)

(x^m)ⁿ = x^mn              (example (2²)³ = 2^{2 x 3} = 2⁶)

x⁰ = 1                        (unless x = 0, then x⁰ = 0)

x¹ = x                        (example 2¹ = 2)

x^-n = 1/xⁿ                 (example 2^-1 = ½)

x^½ = Öx                     (example 9 ^½ = Ö9 = 3, this is a particular case of the next rule)

x^m/n = ⁿÖx^m                    (example 8^2/3 = ³Öx², i.e. the cubed root of 8 squared = 4)

Remember that these rules will apply when m and n are equal to any number.

b) It can be difficult to learn rules like these, so the best thing to do is try solving lots
    of problems on indices. The more you do, the more you will find that you have
    naturally learned the rules anyway (this is the easy way to learn them).

c) You will need to know the rules of indices to solve all sorts of problems in algebra, so
    it's well worth learning the rules properly.

Solve the following: