Question

How do you multiply and simplify `\frac { \root[ 3] { a ^ { 2} } \cdot \root [ 3] { b ^ { 5} } } { \root [ 3] { a b ^ { 2} } }`?

Answer 1

`b root(3)a`

Explanation:

`[root(3)(a^2)* root(3)(b^5)]/root(3)(ab^2) = [a^(2/3)* b^(5/3)]/[a^(1/3)b^(2/3)]`

`rArr a^(2/3)*a^(-1/3)*b^(5/3)*b^(-2/3)` [Note : `1/a^(1) = a^(-1)]`

`rArr a^(2/3-1/3)*b^(5/3-2/3)`

`rArr a^(1/3)*b^(3/3)`

`rArr a^(1/3)*b`

`rArr b root(3)a`