How do you simplify $root7(640 )$ ?

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Answer 1 · 2016-12-23T08:23:01

$root(7)(640) = 2root(7)(5)$

There are a couple of properties that hold for any $n$ th root (where $n$ is a positive integer), including $7$ th roots:

$root(n)(ab) = root(n)(a)root(n)(b)" "$ when $a, b >= 0$

$root(n)(a^n) = a" "$ when $a >= 0$

Factorising $640$ , we find:

$640 = 2^7*5$

So:

$root(7)(640) = root(7)(2^7*5) = root(7)(2^7)*root(7)(5) = 2root(7)(5)$

How do you simplify root7(640 )root7(640 )?