SOLUTION: 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 figu

Algebra ->  Exponents-negative-and-fractional -> SOLUTION: 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 figu      Log On


   

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?
Found 2 solutions by checkley77, Earlsdon:
Answer by checkley77(12844) 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

Answer by Earlsdon(6294) 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%5E3+=+5%2A5%2A5=25%2A5+=+125 Answer is + because (+)*(+)*(+)=(+)
-5%5E3+=+-%285%2A5%2A5%29 = -%2825%2A5%29+=+-125 Answer is negative because (-)*(+)*(+)*(+) = (-)
%28-5%29%5E3+=+%28-5%29%2A%28-5%29%2A%28-5%29 = %28%2B25%29%2A%28-5%29+=+-125 Answer is negative because (-)*(-)*(-) = (-)
-%28-5%29%5E3+=+-%28%28-5%29%2A%28-5%29%2A%28-5%29%29 = -%28%2B25%29%2A%28-5%29+=+-%28-125%29=125 Answer is positive because (-)*((-)*(-)*(-)) = (-)((-)) = (+)