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

1 Answer
AA_123
May 1, 2017

#(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)#

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