Power Crazy!

When you multiply a number by itself you say that the number has been squared.

10 squared is shown in maths as 102 and this is a simple shorthand for 10 x 10 (2 tens multiplied by each other).

Similarly, 10 cubed is shown as 103 which is the same as 10 x 10 x 10 (3 tens multiplied by each other).

104 doesn't have a name like squared or cubed and is simply called 10 to the power 4. And the same applies for all the rest; e.g. 28 (2 to the power 8), 310 (3 to the power 10), 16100 (16 to the power 100) etc.

Now, what does 10-4 (ten to the power minus four) mean?

10-4 means the same as 1 / (10 x 10 x 10 x 10).

In the same way 2-3 means the same as 1 / (2 x 2 x 2) = 1 / 23 = 1/8 and so on….

Note that 3-½ is not the same as the opposite of 3½. This is something different and is called the square root. You know that 32 = 3 x 3 = 9. The square root of 9 is the number which needs to be squared to make 9 - hence the square root of 9 is 3. The symbol for the square root of 9 is .

What is 20? Any number to the power 0 = 1.

What is 21? Any number to the power 1 = itself - therefore 21 = 2.

What is 2-1? Any number to the power -1 = 1 / itself - therefore 2-1 = 1/2.

USEFUL BITS

If we use the letter N to represent any number, then:

N0 = 1

N1 = N

N-1 = 1/N

If we also use the letter P to represent any power, then:

Np = N x N x N……..(P times)

N-P = 1 / (N x N x N….(P times))

 

The useful bits that you've just read allow you to use the rules for any numbers or powers. This is how algebra works - all algebra does is give us a simple way of creating rules, scientific theories etc. which can apply to all numbers - to do this we create equations using letters to represent numbers.

So…..you should have now mastered the basics of using powers and have made a start on algebra - not bad going for just a web page.