Simplify [x^3 / y^-6] ^1/3?

[x^3/y^-6]^(1/3) =

x/y^-2 =

x*y^2.

-John

[x^3/y^-6] ^1/3=

(x^3*1/3)/(y^-6*1/3)= x/y^-2 = xy^2

[x^3 / y^-6] ^1/3
= [x^(3*1/3) / y^(-6*1/3)]
= x / y^-2, rationalizing
= x(y^-2)/ y^-2 * y^-2
= x(y^-2) / y

[ x³ y^6 ] ^(1/3) = x y²

[x^3/y^-6]^1/3
= 3√[x^3/y^-6] (3√ = extract the cube root of)
= 3√[x^3/1/y^6]
= 3√[x^3y^6]
= [x^(3/3)][y^(6/3)]
= xy^2

I learned this on my freshman year for algebra..

= (x^3/y^-6)^1/3

= (x^3*y^6)^1/3 because 1/b^-n = b^n

= 3√(x^3*y^6) because b^1/n = n√x

= x*y^2 <-- final answer

[x^3 / y^-6] ^1/3
[(x^3) /(1)/ (y^6)] ^1/3
[(x^3) *(y^6)] ^1/3
[(x^3) *(y^6)] ^1/3
anything raised to the one third equals the cube root of that thing
cube root of [(x^3) *(y^6)] = xy^2

(x³ / y^-6) ^⅓ can be written as:
[x³ * (1/y^-6)] ^ ⅓, which euqals:
[x³ * y^6)] ^ ⅓. Since the power " ³ " is common to both the variables 'x' and 'y', the equation, thus can be written as:

[(xy²)³] ^ ⅓, which equals:
(xy²)^ (³ * ⅓), which gives: (xy²)¹, as the answer. So:
(x³ / y^-6) ^⅓ = (xy²)¹ or (xy²).

The property to use is this:

(x^a)^b = x^(a*b).