How do you simplify #root3(24a^10b^6)#?

1 Answer
Jul 6, 2016

Answer:

#root(3)(24a^10b^6)=2a^3b^2root(3)(3a)#

Explanation:

#root(3)(24a^10b^6#

Now #a^10=a^(3+3+3+1)=a^3xxa^3xxa^3xxa# and #b^6=b^(2+2+2)=b^2xxb^2 xxb^2# and such above is equal to
#root(3)(2xx2xx2xx3xxa^3xxa^3xxa^3xxaxxb^2xxb^2 xxb^2#

= #root(3)(ul(2xx2xx2)xx3xx ul(a^3xxa^3xxa^3)xxaxx ul(b^2xxb^2 xxb^2)#

= #2xxa^3xxb^2xxroot(3)(3xxa)#

= #2a^3b^2root(3)3a#