Question

How do you simplify `root[ 3] { s t ^ { 7} } \root [ 3] { s ^ { 8} t ^ { 9} }`?

Answer 1

See a solution process below:

Explanation:

First, use this rule for radicals to combine the two terms:

`root(n)(color(red)(a)) * root(n)(color(blue)(b)) = root(n)(color(red)(a) * color(blue)(b))`

`root(3)(color(red)(st^7)) * root(3)(color(blue)(s^8t^9)) => root(3)(color(red)(st^7) * color(blue)(s^8t^9)) => root(3)(s^9t^16)`

Now, rewrite the expression and use this rule to factor some of the terms out of the radical:

`root(n)(color(red)(a) * color(blue)(b)) = root(n)(color(red)(a)) * root(n)(color(blue)(b))`

`root(3)(s^9t^16) => root(3)(color(red)(s^9t^15)) * root(3)(color(blue)(t)) => s^3t^5root(3)color(blue)(t)`