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

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

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