How do you simplify root5(-t^10 )5t10?

1 Answer
Oct 6, 2015

root(5)(-t^10) = -t^25t10=t2

Explanation:

If a > 0a>0 and b, c >= 0b,c0, then a^(bc) = (a^b)^cabc=(ab)c

Also root(n)(-a) = -root(n)(a)na=na if n in ZZ is odd.

So root(5)(-t^10) = -root(5)(t^10) = -(t^10)^(1/5) = -t^(10*1/5) = -t^2

We can also see that (-t^2)^5 = (-1)^5*(t^2)^5 = -t^10, so -t^2 is a fifth root of -t^10.