How do you simplify #\root[ 3] { 54a ^ { 12} b ^ { 16} }#?

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Answer 1 · 2017-09-27T13:25:35

See a solution process below:

First, rewrite the expression as:

#root(3)(27a^12b^15 * 2b)#

Now, use this rule for radicals to simplify:

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

#root(3)(color(red)(27a^12b^15) * color(blue)(2b)) =>#

#root(3)(color(red)(27a^12b^15)) * root(3)(color(blue)(2b)) =>#

#3a^4b^5 * root(3)(color(blue)(2b)) =>#

#3a^4b^5root(3)(2b)#