Week 8

This week we are covering the 'power' or 'index' laws in Al-Jabr.

We all know that:

2 x 2 = 2²

The same power notation is also good for variables:

a x a = a²

When doing calculations where numbers are squared, cubed or multiplied by themselves a lot there are some good 'short cuts' that can be used:

a² x a³ = a x a x a x a x a = a⁵ - we notice that we can add up the powers so
a² x a³ = a^{2 + 3} = a⁵

If you are unsure about this try using a 'normal' number like 2 instead of 'a'.

This can be extended to these general rules:

a^m x aⁿ = a^m+n
a^m / aⁿ = a^{m - n}
(a^m)ⁿ = a^mn

For example (2²)³ = (2 x 2) x (2 x 2) x (2 x 2) = 2^{2 x 3 =} 2⁶

As usual, if it does not make sense - ask for help. Also with maths it sometime helps to try a whole lot of similar questions, and then the meaning of it starts to dawn.

The next (Hammer) maths assignment is here - due Tue 27th of March.
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