How do you simplify $root3(16)*root3(4)$ ?

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Answer 1 · 2016-08-22T09:49:56

$root3(16)*root3(4)=4$

$root3(16)*root3(4) = root3(2^4)*root3(2^2)$

$= root3(2^(4+2)) = root3(2^6)$

$=2^(6/3) = 2^2 = 4$

Answer 2 · 2016-08-22T09:58:56

4

Method 1)
$root3(16)*root3(4)$ = $root3(16*4)$ = $root3(64)$ =4

Method2)
$root3(16)$ = $16^(1/3)$
16 = $4^2$

$16^(1/3)$ = $(4^2)^$
= $4^(2/3)$

But $root3(4)$ = $4^(1/3)$
So
$root3(16)*root3(4)$ = $4^(2/3)*4^(1/3)$ =4

How do you simplify root3(16)*root3(4)root3(16)*root3(4)?