Question

How do you simplify `\root[ 3] { 29a ^ { 7} b ^ { 9} c ^ { 10} }`?

Answer 1

See a solution process below:

Explanation:

We can rewrite the expression as:

`root(3)(a^6b^9c^9 * 29ac)`

Using this rule of radicals we can rewrite the expression as:

`root(n)(color(red)(x) * color(blue)(y)) = root(n)(color(red)(x)) * root(n)(color(blue)(y)`

`root(3)(color(red)(a^6b^9c^9) * color(blue)(29ac)) => root(3)(color(red)(a^6b^9c^9)) * root(3)(color(blue)(29ac)) => color(red)(a^2b^3c^3)root(3)(color(blue)(29ac))`