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Exponents with Negative Bases

So far, my examples have been squares...

What if we did cubes with negative bases?

(-5)^3 and -5^3

Are these going to be the same? 

Let's just write out what each one means and see what happens.

(-5)^3 = (-5)(-5)(-5) = -125
The parenthesis means that the
negative is locked in the box with the 5.

-5^3 = - 5 x 5 x 5 = -125
The negative stays out in front.

Hey, both answers are negative this time!  So, these ARE the same!

The key is to always remember what these means and what's going on and you'll never go wrong.

YOUR TURN:

Work through these...  Do you see a pattern in the answers?  See what's going on?

(-2)^1 ... (-2)^2 ... (-2)^3 ... (-2)^4 ... (-2)^5

-2^1 ... -2^2 ... -2^3 ... -2^4 ... -2^5