How do you simplify #(6py^2)^(1/4)#?

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Answer 1 · 2017-07-31T12:50:23

See a solution process below:

First, rewrite the expression using this rule of exponents:

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

#(6py^2)^(1/4) => (6^color(red)(1)p^color(red)(1)y^2)^(1/4)#

Now, use this rule of exponents to eliminate the outer exponent:

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

#(6^color(red)(1)p^color(red)(1)y^color(red)(2))^color(blue)(1/4) =>#

#6^(color(red)(1)xxcolor(blue)(1/4))p^(color(red)(1)xxcolor(blue)(1/4))y^(color(red)(2)xxcolor(blue)(1/4)) =>#

#6^(1/4)p^(1/4)y^(1/2)#

Or

#(6p)^(1/4)y^(1/2)#

Or

#root(4)(6p)sqrt(y)#