How do you simplify #\root[ 3] { 16} \cdot \root [ 4] { 32}#?

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Answer 1 · 2017-09-26T12:51:50

See a solution process below:

First, rewrite and simplify each radical as:

#root(3)(8 * 2) * root(4)(16 * 2) =>#

#(root(3)(8)root(3)(2)) * (root(4)(16)root(4)(2)) =>#

#(2root(3)(2)) * (2root(4)(2))#

Now, we can rewrite and simplify as:

#2 * root(3)(2) * 2 *root(4)(2) =>#

#2 * 2 * root(3)(2) * root(4)(2) =>#

#4root(3)(2)root(4)(2)#

If necessary, we can further simplify as:

#4 * 2^(1/3) * 2^(1/4) =>#

#4 * 2^(1/3 + 1/4) =>#

#4 * 2^(4/12 + 3/12) =>#

#4 * 2^(7/12) =>#

#4 * 2^(7 * 1/12) =>#

#4 * (2^7)^(1/12) =>#

#4 * (128)^(1/12) =>#

#4 * root(12)(128) =>#

#4root(12)(128)#