Question

How do you simplify `\sqrt { 121a ^ { 6} b ^ { 4} c ^ { 32} }`?

Answer 1

See a solution process below:

Explanation:

First, rewrite this expression as:

`sqrt(11^2a^6b^4c^32) => (11^2a^6b^4c^32)^(1/2)`

Next, use this rule of exponents to simplify this expression:

`(x^color(red)(a))^color(blue)(b) = x^(color(red)(a) xx color(blue)(b))`

`(11^color(red)(2)a^color(red)(6)b^color(red)(4)c^color(red)(32))^color(blue)(1/2) = 11^(color(red)(2) xx color(blue)(1/2))a^(color(red)(6) xx color(blue)(1/2))b^(color(red)(4) xx color(blue)(1/2))c^(color(red)(32) xx color(blue)(1/2)) =`

`11^1a^3b^2c^16`

Now, use this rule of exponents to complete the simplification:

`a^color(red)(1) = a`

`11^color(red)(1)a^3b^2c^16 = 11a^3b^2c^16`