How do you evaluate # 48^(4/3)*8^(2/3)*(1/6^2)^(3/2) #?

1 Answer
May 2, 2016

#48^(4/3)* 8^(2/3)*(1/6^2)^(3/2)=2^(13/3)/3^(1/3)#

Explanation:

#48^(4/3)* 8^(2/3)*(1/6^2)^(3/2)#

= #(2xx2xx2xx2xx3)^(4/3)* (2xx2xx2)^(2/3)*((2xx3)^(-2))^(3/2)#

=#(2^4xx3)^(4/3)* (2^3)^(2/3)*(2xx3)^(-2xx3/2)#

= #2^(4xx4/3)*3^(4/3)*2^(3*2/3)*(2xx3)^(-3)#

= #2^(16/3)* 3^(4/3)* 2^2*2^(-3)*3^(-3)#

= #2^(16/3+2-3)xx3^(4/3-3)#

= #2^(13/3)xx3^(-1/3)#

= #2^(13/3)/3^(1/3)#