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If you are puzzled by this, don't be, as I will attempt to clarify these sequences
above. To begin, note that counting in base 10 involves the 10 symbols 0, 1, 2, 3, 4, 5, 6,
7, 8 and 9. The number 23 in base 10 has 2 and a 3, where the 2 represents 10s and the 3
represents units or 1s. If we consider the number 328 in base 10, the 3 stands for hundreds
or 10 x 10, the 2 represents tens and the 8 stands for units. Hundreds, tens and units are
all powers of 10 as the hundreds represent 10 to the second power, the ten represents 10
to the first power and unit represents 10 to the zero power. Any positive whole number to
the zero power is 1, whether it be 10, 16, 8 or 2. Trust me.
This you may have learned in math when you studied powers of numbers. If you
missed that class a quick lesson in factors and powers should convince you of this.
Powers of a number are nothing more than the number of times it is used as a factor. Thus
10 x 10 x 10
uses 10 as a factor three times or we could say that this represents
10 to the power of 3,
or
10 to the 3rd power.
If we divide
10 x 10 x 10
or
10 to the 3rd power
by
10 x 10
or
10 to the 2nd power,
the result is 10 since we are dividing 1000 by 100 and we know that the result is simply
10. You may have also learned that you could accomplish the division by merely
subtracting the exponents or powers of 10. In this case we would subtract 2 from 3 giving
1 and we would still come up with 10, or 10 to the 1st power.
With that in mind, consider dividing
10 x 10 x 10
by
10 x 10 x 10
or
10 to the 3rd power
by
10 to the 3rd power.
Subtracting the exponents 3 from 3 gives 0 or our answer is
10 to the 0 power.
But we know that 1000 divided by 1000 is equal to 1 which illustrates that
10 to the 0 power
is equal to 1. Didn't I tell you? If we did a similar division using a 6 rather than the 10
you could see that any positive number to the 0 power will be equal to 1. Note however
that 0 to the 0 power is not equal to 1!
This brings us back to our number 328, which is
