Question

Simplify the following
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Answer 1

Answer:

$\frac{ {x}^{2m + 2n} \times {x}^{2n + 2p} \times {x}^{2p + 2m} }{ { ({x}^{n + m + p}) }^{3} } \\ = \frac{ {x}^{2m + 2n + 2n + 2p +2p +2m } }{ {x}^{3n + 3m + 3p} } \\ = \frac{ {x}^{4m + 4n + 4p} }{ {x}^{3m + 3n + 3p} } \\ = {x}^{4m + 4n + 4p - (3m + 3n + 3p)} \\ = {x}^{4m + 4n + 4p - 3m - 3n - 3p} \\ = {x}^{m + n + p}$

Properties used here are -

(x^m)^n = x^mn

x^m × x^n = x^m+n

x^m / x^n = x^m-n