Posted by **Hannah** on Monday, September 6, 2010 at 7:49pm.

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**, Monday, September 6, 2010 at 7:53pm
(-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**, Monday, September 6, 2010 at 7:59pm
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.

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