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
