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

Question

1595 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 $64(x^4y^3)^(5/6)$

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

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

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

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

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

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

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

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

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