How do you write #root4(2^6)# as a radical?

Question

1370 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-06-11T21:14:29

See a possible solution process below:

This expression is already written as a radical. If you want to simplify this expression we can use the following process:

#root(4)(2^6) = root(4)(2^4 * 2^2) = root(4)(2^4) * root(4)(2^2) = 2 * root(4)(4) = 2root(4)(4)#

If you want to write this expression using exponents you can use this rule of radicals and exponents to rewrite this expression:

#root(color(red)(n))(x) = x^(1/color(red)(n))#

#root(color(red)(4))(2^6) = (2^6)x^(1/color(red)(4))#

We can now use this rule of exponents to simplify the expression:

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

#(2^color(red)(6))^color(blue)(1/4) = 2^(color(red)(6) xx color(blue)(1/4)) = 2^(6/4) = 2^(3/2)#