(3x216)^(2/3) ··· Ex.1*** Factor 3x216 by the prime numbers:
3x216=3x2x2x2x3x3x3=(2^3)x(3^4) Square 3x216:
(3x216)^2={(2^3)^2}x{3^4)^2}=(2^6)x(3^8)=(2^6)x(3^6)x(3^2) Take the cube root of (3x216)^2:
{(3x216)^2}^(1/3)={(2^6)x(3^6)x(3^2)}^(1/3)=(2^2)x(3^2)x{9^(1/3)} We have:
(3x216)^(2/3)=4x9x{9^(1/3)}=36 x 9^(1/3)
The answer is: (3x216)^(2/3) = 36 x 9^(1/3) (= approx 74.883)
*** If this question is asking the value of 3x{(216)^(2/3)}, the answer is:
3x{(216)^(2/3)} = 3 x {(2^3)x(3^3)}^(2/3) = 3 x (2^2) x (3^2) =3x4x9=108
The answer is: 3x{(216)^(2/3)}=108