How do you simplify #\root[ 3] { 49x ^ { 2} } \times \root [ 3] { 56xy ^ { 3} }#?

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Answer 1 · 2017-10-09T12:36:38

See a solution process below:

First, use this rule for radicals to rewrite the expression:

#root(n)(color(red)(a)) * root(n)(color(blue)(b)) = root(n)(color(red)(a) * color(blue)(b))#

#root(3)(color(red)(49x^2)) * root(3)(color(blue)(56xy^3)) =>#

#root(3)(color(red)(49x^2) * color(blue)(56xy^3))#

#root(3)(2744x^3y^3) =>#

#root(3)(343 xx 8 xx x^3y^3) =>#

#root(3)(7^3 xx 2^3 xx x^3y^3) =>#

#root(3)(7^3)root(3)(2^3)root(3)(x^3y^3) =>#

#7 xx 2 xx xy =>#

#14xy#