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:

_{}

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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.