SOLUTION: (-5a^2)(-5a^3)^4 simplified, the answer is (-5)^5a^14. What I don't understand is, how did the negative sign shift to the 5 only? Please explain. Thanks

Algebra ->  Expressions -> SOLUTION: (-5a^2)(-5a^3)^4 simplified, the answer is (-5)^5a^14. What I don't understand is, how did the negative sign shift to the 5 only? Please explain. Thanks      Log On


   

Question 120491: (-5a^2)(-5a^3)^4 simplified, the answer is (-5)^5a^14.
What I don't understand is, how did the negative sign shift to the 5 only? Please explain. Thanks
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
(-5a^2)(-5a^3)^4 simplified, the answer is (-5)^5a^14.
What I don't understand is, how did the negative sign shift to the 5 only? Please explain.
-------------
(-1) raised to an even power is 1
(-1) raised to an odd power is negative
-------------
Your problem:
(-5a^2)(-5a^3)^4
The -5 in the 1st factor is raised to the power one which is odd
so the negative survives.
The -5 in the 2nd factor is raised to the power 4 which is even
so the negative becomes positive.
---------------
(-5a^2)(-5a^3)^4
= (-5a^2)[(-5)^4(a^3)^4]
= (-5)(a^2)(-5)^4(a^12)
= (-5)^5(a^14)
===============
Cheers,
Stan H.