How do you simplify #64(x^{4}y^{3})^{\frac{5}{6}}#?

Question

1418 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-06-23T12:48:43

#64(x^4y^3)^(5/6)=64x^3y^2root(3)xsqrty#

Remember #(ab)^m=a^mb^m# and #(a^m)^n=a^(mn)#

Hence #64(x^4y^3)^(5/6)#

= #64xx(x^4)^(5/6)xx(y^3)^(5/6)#

= #64xx x^(4xx5/6)xxy^(3xx5/6)#

= #64xx x^(20/6)xxy^(15/6)#

= #64xx x^((color(red)2xx10)/(color(red)2xx3))xxy^((color(red)3xx5)/(color(red)3xx2))#

= #64xx x^(10/3)xxy^(5/2)#

= #64xx x^(3+1/3)xxy^(2+1/2)#

= #64xx x^3x^(1/3)y^2y^(1/2)#

= #64x^3y^2root(3)xsqrty#