Basic equation simplification of power series

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Is $$(x^1+x^2+x^3...)^5$$ equal to $$x^5(1+x+x^2+...)^5$$

If so, how? can someone tell me the steps involved in taking the x out? The expression is raised to a power, so how can one simply take x out without expanding? Maybe it is something basic but I don't know how it is done? Thanks in advance.

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Use $a^5b^5 =(ab)^5$

Second one is $$x^5(1+x+x^2+...)^5 = \Big(x(1+x+x^2+...)\Big)^5 = (x+x^2+x^3+...)^5$$