Circle the value of 𝑥 which makes 6.4 multiplied by 10 to the power of 𝑥 a cube
number. Is it zero, one, two, or three?
Let’s begin by reminding ourselves what we mean by a cube number. A cube number is the result of multiplying an integer by itself and then by itself
again. So one is a cube number because it’s the result of one multiplied by one multiplied
by one. The second cube number is eight. That’s the result of two multiplied by two multiplied by two.
It’s important to know by heart the first five cube numbers, but we can work them
out. The third cube number is 27. That’s three multiplied by three multiplied by three. Four multiplied by four multiplied by four is 64. And five multiplied by five multiplied by five is 125.
Notice how the fourth cube number looks a little like the one in our question. The keyword in our definition though was the word “integer.” That’s a whole number. And at the moment, 6.4 is not a whole number. So it can’t be the result of multiplying an integer by itself and then by itself
In fact, let’s see what happens if 𝑥 was equal to zero. Our number will become 6.4 times 10 to the power of zero. Anything to the power of zero is one. So 6.4 multiplied by 10 to the power of zero is 6.4 multiplied by one, which is
6.4. So when 𝑥 is zero, we don’t get a cube number from 6.4 multiplied by 10 to the power
Let’s try the next value for 𝑥. If 𝑥 was one, our sum becomes 6.4 times 10 to the power of one. Now anything to the power of one is itself, so 10 to the power of one is simply
10. And when we multiply by 10, we move the digits to the left one space. This means that the six, which is currently in the units column, moves to the tens
and the four that’s currently in the tenths column moves to the units. 6.4 multiplied by 10 is 64, which we know is a cube number. So we found our solution. The value of 𝑥 which makes 6.4 times 10 to the power of 𝑥 a cube number is one.