How do you simplify #(x^6)^(1/2)#?

Question

4826 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-02-16T22:44:27

#x^3#

#(x^6)^(1/2)# may also be written as #" "x^(6xx1/2) = x^(6/2) = x^3#

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
By the way #(x^6)^(1/2)# is another way of writing #sqrt(x^6)#

Answer 2 · 2017-02-16T23:58:07

#(x^6)^(1/2) = abs(x^3)#

Note that if #t >= 0# then #sqrt(t^2) = t#

If #t < 0# then #sqrt(t^2) = -t#

To cover both these cases we can write:

#sqrt(t^2) = abs(t)#

Putting #t = x^3# we find:

#(x^6)^(1/2) = sqrt(x^6) = sqrt((x^3)^2) = abs(x^3)#