Question

How do you simplify `((8x^3 )/ (27y^6))^(1/3)`?

Answer 1

`(2x)/(3y^2)`

Explanation:

`((8x^3)/(27y^6))^(1/3)` is the same as `((color(green)(2^3)x^3)/(color(green)(3^3)y^6))^(1/3)`

Distribute the external exponent `(color(red)(1/3))`into the exponents inside (for both numerator and the denominator)

`((color(green)(2^3)x^3)/(color(green)(3^3)y^6))^color(red)(1/3)=(color(green)(2^(3*color(red)(1/3)))x^(3*color(red)(1/3)))/(color(green)(3^(3*color(red)(1/3)))y^(6*color(red)(1/3)))=(color(green)2x)/(color(green)3y^2)`