SOLUTION: I haven't seen this math in years. Can you help me please. What does it mean to simply the expression. Question: -3 (with a -2 in higher power) and also again when it's in

Algebra ->  Square-cubic-other-roots -> SOLUTION: I haven't seen this math in years. Can you help me please. What does it mean to simply the expression. Question: -3 (with a -2 in higher power) and also again when it's in      Log On


   



Question 99561: I haven't seen this math in years.
Can you help me please. What does it mean to simply the expression.
Question:
-3 (with a -2 in higher power) and also again when it's in ()
(-3) (also with a -2 in higher power).
Thanks

Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
I haven't seen this math in years.
Can you help me please. What does it mean to simply the expression.
Question:
-3 (with a -2 in higher power) and also again when it's in ()
(-3) (also with a -2 in higher power).
Thanks
You are wanting to know the difference between

-3%5E%28-2%29 and %28-3%29%5E%28-2%29

Notice that the first begins with a negative sign "-"
whereas the second begins with "(".

When an expression begins with a negative sign, consider
that introductory "-" as though it were "-1×"

So

-3%5E%28-2%29 means -1×3%5E%28-2%29

Then we use the rule for negative exponents
and replace only the 3%5E%28-2%29 factor by 1%2F3%5E2

Therefore

-1×3%5E%28-2%29 means -1×1%2F3%5E2

which means -1×1%2F9 which means -1%2F9

-------------------------------------

Now %28-3%29%5E%28-2%29 does not begin with a negative sign,
so we go ahead and begin with using the rule for negative 
exponents and therefore

%28-3%29%5E%28-2%29 means 1%2F%28-3%29%5E2

Since -3%29%5E2 means %28-3%29%28-3%29 which is +9

%28-3%29%5E%28-2%29 means 1%2F%28-3%29%5E2 which means 1%2F9

-------------------------

Note that the difference is in the sign.  One rule that
always works is: 

1. if the power is EVEN the answer to
the one that begins with a "-" is negative and
the one that begins with "(" is positive.

2. if the power is ODD the answers to
both are the same, and that answer is always negative. 

Yours was case 1 with an EVEN exponent, so they ended
up with different signs.  However if you had had an ODD 
exponent they would have both ended up as the same 
NEGATIVE number.

Edwin