Simplify and evaluate. Use only positive exponents.
-32=?

This is tricky. The answer is -9.

(-3)2 is +9 but -32 is -9

Why is this?

When there is a negative sign " - " in front it always
means "negative one times" or " -1× "

So when you see

-32 

you must think of it as

-1×32

Then you must do the exponent 2 first,

replacing the 32 by 9, getting

-1×9

Then you do the multiplication, getting

-9.

On the other hand, if you see this:

(-3)2 

Then you must think of it as

(-3)(-3)

which give you +9 or just 9.

I realize that is confusing but you'll get
used to it.

If you have -24 that means -1×24 which
is -1×2×2×2×2 or -16.

But if you see (-2)4 that means (-2)(-2)(-2)(-2)
which is +16.

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Now as it turns out, if you see

-23 that means -1×23 or -1×2×2×2 = -8

and if you see (-2)3 that means (-2)(-2)(-2) = -8

So when the exponent is odd, they turn out to be the
same!  

But when the exponent is even, they are different.

Edwin