Video: GCSE Mathematics Foundation Tier Pack 1 β€’ Paper 3 β€’ Question 4

GCSE Mathematics Foundation Tier Pack 1 β€’ Paper 3 β€’ Question 4

03:50

Video Transcript

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

Another way of writing π‘Ž multiplied by π‘Ž multiplied by π‘Ž is π‘Ž cubed or π‘Ž to the power of three. This just means π‘Ž multiplied together three times. To find the value of π‘Ž, we need to find the cubed root of each side of this equation. So we have that π‘Ž 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‘Ž 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‘Ž 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 you’re 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 it’s 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. It’s π‘₯ and then a little box where the superscript power will go. But on some calculators, it’s π‘₯ and then a superscript 𝑦. 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 it’s 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 𝑦 button, you would have to press the three first then this button and then five. Now you don’t have to use this button as, as we’ve 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 wouldn’t 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 let’s 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.

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