Question

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

Answer 1

`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`