Posted by Hannah on .
Simplify each expression
(216)^1/3
My answer is 1/6. Am I correct.
(x^4y)^1/3 (xy^4)^2/3
I do not know how to simplify this.

Math 
Reiny,
(216)^1/3 =  1/6
(how can (1/6)(1/6)(1/6) end up negative ?
(x^4y)^1/3 (xy^4)^2/3
= (x^(13))(y^(1/3))(x^(2/3))(y^(8/3)
= x^2 y^3 
Math 
MathMate,
1/6 is almost correct, except that you probably notice the original expression is negative. Give it one more try.
Use the rules of exponentiation:
(ab)^(m/n)=(a^m * b^m)^(1/n)
and the inverse:
(a^m)(1/n)
=(a^(m/n))
So
(x^4y)^2/3 (xy^4)^1/3
=( (x^4y)^2 * (xy^4) )^(1/3)
=( x^8*y^2 * x * y*4 )^(1/3)
=(x^9 * y^6)^(1/3)
=x^3 * y^2
(Note that the above example is not the same as the given question).
Post your answer for a check if you wish.