10.1.4 Zero as a Power

Notepad iconActivity: Zero as a Power

Work out 10 cubed division 10 cubed the “long way” and using the rules that we have just learned about.

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Answer

equation sequence 10 cubed division 10 cubed equals 10 cubed divided by 10 cubed equals 10 multiplication 10 multiplication 10 divided by 10 multiplication 10 multiplication 10 equals one divided by one equals one

The powers rule gives equation sequence 10 cubed division 10 cubed equals 10 super open three minus three close equals 10 super zero. So it follows that 10 super zero equals one. But what does 10 super zero mean? “10 multiplied by itself zero times” does not make sense, so 10 super zero is defined as having the value 1. You can use a similar argument to show that any number to the power zero has a value of 1. For example, two super zero equals one, 3.25 super zero equals one, and open six minus close super zero equals one.

Now let’s take a look at negative exponents or powers.

10.1.3 Multiplying and Dividing Numbers with the Same Base Number

10.1.5 Negative Exponents