### Video Transcript

Consider the equation π multiplied
by π multiplied by π is equal to 729. Part a) Find the value of π.

Another way of writing π
multiplied by π multiplied by π is π cubed or π to the power of three. This just means π multiplied
together three times. To find the value of π, we need to
find the cubed root of each side of this equation. So we have that π is equal to the
cubed root of 729. This just means what value do we
multiply together three times to get 729.

We can use a calculator to evaluate
this. On most calculators, the cubed root
function is situated above the square root button. And you have to press shift first
in order to get to it. If you press shift and then the
square root button, you should see the cube root icon appear, which is a square root
sign with a little three on the outside. Typing this into our calculator
gives the answer nine, so the value of π is nine.

Now we can check our answer by
working out what nine multiplied by nine multiplied by nine is equal to. First of all, nine multiplied by
nine is equal to 81, so we have 81 multiplied by nine. This is equal to 729, so our value
of π is correct.

Part b) Calculate three to the
power of five. Now I said this automatically when
I read the question out. But remember that three and then a
small superscript five means three to the power of five. This just means three multiplied
together five times: three multiplied by three multiplied by three multiplied by
three multiplied by three.

We can use a calculator to evaluate
this, and we have a choice of methods to use. Firstly, we could just type this
directly into our calculator. If youβre going to do it that way,
make sure you count the number of threes that you type in carefully. You must make sure there are five
of them. It gives 243.

The other option is to use the
power button on your calculator. Now what this button looks like and
where itβs positioned will vary depending on what type of calculator you have. But as long as your calculator is a
scientific calculator, you should have a button somewhere.

On my calculator, it looks like the
second of these two buttons. Itβs π₯ and then a little box where
the superscript power will go. But on some calculators, itβs π₯
and then a superscript π¦. On my calculator, I have to type
three first then press this power button and then five. If I do this, what appears on the
calculator display is three and then itβs a little hat or circumflex and then a
five. And if I press equals, it gives
243, which is the value we found by doing the calculation longhand.

Similarly, if your calculator has
an π₯ to the power of π¦ button, you would have to press the three first then this
button and then five. Now you donβt have to use this
button as, as weβve seen, you get the same result if you type the calculation in
longhand. But if it was a very large power,
for example, 20, you wouldnβt want to type in three multiplied by three multiplied
by three 20 times. So the power button just gives us a
shortcut to use.

Now letβs just do another little
check to make sure our answer is correct. Three multiplied by three, first of
all, gives nine. Multiplying nine by three gives
27. Multiplying 27 by three gives
81. And finally, multiplying 81 by
three gives 243. Three to the power of five is equal
to 243.