Powers and Roots, and BODMAS

Today in class we had a look at what a power and a root are.

First we looked at powers. Now you may have seen something that looks kind of like this before:

5²

This just looks like a number 5 with a small number 2 on the right hand side of it. In maths, when we see something like this we say "five raised to the power of two". What this basically means is we want to multiply 5 by itself two times. So: 5 x 5 = 25

Now we could have something different, such as 6⁵

We say this one as "six raised to the power of five", and it simply means 6 multiplied by itself 5 times. So: 6 x 6 x 6 x 6 x 6 = 7776

Now we also have stuff that looks like this: 

In maths, we say this as the "square root of twenty-five". What this is basically asking us for is a number, that when multiplied by itself twice (because of the little two on the left) will equal 25. So in this case, we know 5 x 5 = 25, or 5 multiplied by itself twice is equal to 25, so the answer to our problem is 5. 

We could also get something that looks like this:

We can describe this one as the "third root of 64". In simpler terms, this is asking us what number, multiplied by itself 3 times, is equal to 64. We can work out that 4 x 4 x 4 = 64, or 4 multiplied by itself three times is equal to 64. So the answer to our problem is 4. 

Now finally today we had a look at order of operations. In maths, when we are faced with a problem we must solve it in a particular order. This is where order of operations comes in. A good acronym to remember is BODMAS. This stands for: 

Now we use this because it actually tells us the order we need to solve our problems. We must first solve any brackets, then followed by any Orders (basically what we were looking at above, so powers and roots). Next we solve any Division or Multiplication. These may be written as separate words, but they are really grouped together. Finally, we solve any Addition or Subtraction. Again, these are written separately but they are actually grouped together. 

The following website has some great examples. It does use a slightly different acronym (PEMDAS), however it is all the same in the end. 

http://www.mathsisfun.com/operation-order-pemdas.html 

For homework, continue working through the sheet. Remember this needs to be finished before the end of term. 

As always, feel free to comment on here if you have any questions, or email or chat to me in person.