Question #45348

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Answer 1 · 2017-03-17T16:11:29

$16^(2/3)$ can be rewritten as $root(3) (16^2)$

Solve for the inside first:

$16^2=256$

Now take the third root of this. Break down 256 into powers of 2:

$256=2^8$

$8$ goes into $3$ 2 times and you have a remainder of $2^2=4$ So we have:

$2*2 root(3)(4)$

Answer 2 · 2017-03-17T16:30:35

$4root(3)(2^2)$

Before you do anything else it is wise to look and see if you can spot any short cuts. I have spotted 1

Just accept that $16^(2/3)$ is another way of writing $root(3)(16^2)$

When ever you have a root check to see if there are any values you can 'extract' from it. In this case we would be looking for cubed value.

$16=4^2=2^2xx2^2 = 2^3xx2$ so

$16^2=2^3xx2xx2^3xx2=2^3xx2^3xx2^2$

$root(3)(16^2)->root(3)(2^3xx2^3xx2^2)" "=" "2xx2xxroot(3)(2^2)" "=" "4root(3)(2^2)$