How do you simplify #\frac { ( 9s ^ { - 5} t ^ { 4} ) ^ { 3/ 2} } { ( 27s ^ { 6} t ^ { - 2} ) ^ { 2/ 3} }#?

1 Answer
Jan 9, 2018

Answer:

Assuming #s# and #t# are both positive;

#((9s^(-5)t^4)^(3/2))/((27s^6t^(-2))^(2/3))=(3t^(22/3))/s^(23/2)#

Explanation:

#((9s^(-5)t^4)^(3/2))/((27s^6t^(-2))^(2/3))=((3^2s^(-5)t^4)^(3/2))/((3^3s^6t^(-2))^(2/3)#

#((3^2s^(-5)t^4)^(3/2))/((3^3s^6t^(-2))^(2/3))=(3^3s^(-15/2)t^6)/(3^2s^4t^(-4/3))#

#(3^3s^(-15/2)t^6)/(3^2s^4t^(-4/3))=3^(3-2)s^((-15-8)/2)t^((18-(-4))/3#

#3^(3-2)s^((-15-8)/2)t^((18-(-4))/3)=3s^(-23/2)t^(22/3)#

#3s^(-23/2)t^(22/3)=(3t^(22/3))/s^(23/2)#

Hope it helps :)