Question

How do you simplify `\root [ 5] { 192x ^ { 7} y ^ { 20} }`?

Answer 1

See explanation below

Explanation:

`root(5)(192x^7y^20) = (192x^7y^20)^(1/5)`

There is a rule of exponents which states:

`color(red)((x^a)^b = x^(a*5)`

We can use this rule to further simplify.

`(192x^7y^20)^(1/5) = 192^(1/5)x^(7*1/5)y^(20*1/5) =`

`192^(1/5)x^(7/5)y^4`