Questions on Algebra: Negative and Fractional exponents answered by real tutors!

Algebra ->  Algebra -> Questions on Algebra: Negative and Fractional exponents answered by real tutors!     (Log On)
Ad: Algebra Solved!™: algebra software that solves YOUR algebra homework problems with step-by-step help!



Question 156213: please help my daughter.
What is the difference between the following..
5^3, -5^3, (-5)^3, and finally -(-5)^3. I have never been good with arithmatic, and cannot seem to figure out what is positive, and negative, or how to come to any conclusions here. I know some answers will be +125, but which are negative and why?
: please help my daughter.
What is the difference between the following..
5^3, -5^3, (-5)^3, and finally -(-5)^3. I have never been good with arithmatic, and cannot seem to figure out what is positive, and negative, or how to come to any conclusions here. I know some answers will be +125, but which are negative and why?

Answer by checkley77(3848) About Me  (Show Source):
You can put this solution on YOUR website!
5^3
5*5*5=125
-5^3
-(5*5*5)=-125
(-5)^3
-5*-5*-5=-125
-(-5)^3
-(-5*-5*-5*)-(-125)=125
Question 156213: please help my daughter.
What is the difference between the following..
5^3, -5^3, (-5)^3, and finally -(-5)^3. I have never been good with arithmatic, and cannot seem to figure out what is positive, and negative, or how to come to any conclusions here. I know some answers will be +125, but which are negative and why?
: please help my daughter.
What is the difference between the following..
5^3, -5^3, (-5)^3, and finally -(-5)^3. I have never been good with arithmatic, and cannot seem to figure out what is positive, and negative, or how to come to any conclusions here. I know some answers will be +125, but which are negative and why?

Answer by Earlsdon(3816) About Me  (Show Source):
You can put this solution on YOUR website!
Remember the rule!
When you multiply or divide two numbers that have the same sign, (+,+) or (-,-), the answer is positive.
When you multiply or divide two numbers that have opposite signs, (+,-) or (-,+), the answer is negative.
5^3 = 5*5*5=25*5 = 125 Answer is + because (+)*(+)*(+)=(+)
-5^3 = -(5*5*5) = -(25*5) = -125 Answer is negative because (-)*(+)*(+)*(+) = (-)
(-5)^3 = (-5)*(-5)*(-5) = (+25)*(-5) = -125 Answer is negative because (-)*(-)*(-) = (-)
-(-5)^3 = -((-5)*(-5)*(-5)) = -(+25)*(-5) = -(-125)=125 Answer is positive because (-)*((-)*(-)*(-)) = (-)((-)) = (+)