How do you simplify #\frac { 5\root[ 4] { 162} } { \root [ 4] { 2} }#?

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Answer 1 · 2017-07-17T22:44:05

See a solution process below:

First, rewrite the term in the radical in the denominator as:

#(5root(4)(81 * 2))/root(4)(2)#

Next, use this rule for radicals to rewrite and simplify the expression:

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

#(5root(4)(color(red)(81) * color(blue)(2)))/root(4)(2) => (5root(4)(color(red)(81))root(4)(color(blue)(2)))/root(4)(2)#

We can now cancel common terms in the numerator and denominator:

#(5root(4)(color(red)(81))cancel(root(4)(color(blue)(2))))/color(blue)(cancel(color(black)(root(4)(2)))) => 5root(4)(color(red)(81))#

Now, the fourth root of #81# is #3# so we can write this expression as:

#5root(4)(color(red)(81)) = 5 * 3 = 15#