What is #a^(1/2)b^(4/3)c^(3/4)# in radical form?

1 Answer
smendyka
Jul 20, 2017

See a solution process below:

Explanation:

First, rewrite the expression as:

#a^(1/2)b^(4 xx 1/3)c^(3 xx 1/4)#

We can then use this rule of exponents to rewrite the #b# and #c# terms:

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

#a^(1/2)b^(color(red)(4) xx color(blue)(1/3))c^(color(red)(3) xx color(blue)(1/4)) => a^(1/2)(b^color(red)(4))^color(blue)(1/3)(c^color(red)(3))^color(blue)(1/4)#

We can now use rule to write this in radical form:

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

#root(2)(a)root(3)(b^4)root(4)(c^3)#

Or

#sqrt(a)root(3)(b^4)root(4)(c^3)#

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