You’ve got to be extra careful when you’re calculating what a negative number raised to a power is. For instance, if I had:
This is the same as
Since we know that a negative number multiplied by another negative number gives a positive number, we can write that
However, we can also get negative answers. For instance:
This is the same as
which we can do in two parts:
Luckily, there is an easy trick for calculating the result of raising a negative number to a power:
Handy Hint #1 - Powers of negative numbers
If you raise a negative number to an even power (such as 2, 4, 6, 8 etc...) then the answer will be positive.
But if you raise a negative number to an odd power (such as 1, 3, 5, 7 etc…) then the answer will be negative.
Look at the last two examples – when we raised ‘–2’ to an even power (2), we got a positive answer. When we raised ‘–2’ to an odd power (3), we got a negative answer.