Mar 6, 2012

Powers of Math!

Alright.. after a prolonged break (sorry), I am now ready to guide you into the realm of powers.
It's really quite easy, and even fun.
Powers are to multiplication, as multiplication is to addition. In other words, powers are simply the same number multiplied several times.
5x5x5 is an example, although it is generally written as 5^3...

There is no real shortcut for doing powers. So generally, you will just have use multiplication principles.
In the above formula, 5^3.. you would multiply 5 by itself 3 times... like this..
5x5=25.... 25x5=125   (this may seem a bit weird, but what you're doing is multiplying the previous multiplication by 5, which is how it is supposed to be)

Since powers are simply specific multiplication problems, it doesn't take much more to explain it..
Just remember. The number after the ^ sign.. is simply how many times you are multiplying the number.
If it helps, for the problem Y^X.. simply write down X number of Ys. Then multiply.

Now, for a little secret that will help speed up the process.
When you have a number to the power of 4 or more, it is often easier to multiply in chunks, then multiply the chunks together... like this;
4^4.. you could multiply it out 4 times.. OR you can break it down into 2 chunks of 4x4.. getting 16x16...
You can probably answer 4x4 in your head, and 16x16 is pretty easy to multiply as well. Plus, you're only doing 2 multiplications (because doing 4x4 twice doesn't require doing the math again.. you KNOW that 4x4 will always equal 4x4)

If you did it the other way, you would have to do 3 separate multiplications. 4x4... 16x4 and 64x4

To put this into formulatic terms
Y^X =  Y^X/2 x Y^X/2 OR
Y^X=  Y^X/3 x Y^X/3 x Y^X/3 ... etc.

OK.. this week's problems!


(note: these are all fairly easy, and you should be able to do each one within 1-2 minutes)