Final answer:
To simplify the expression (2x^c)/{(ax^4)^b}, you apply the Power of a Power Rule and Division Rule of exponents, resulting in (2/a^b) * x^(c-4b).
Step-by-step explanation:
The given expression is (2x^c)/{(ax^4)^b}. To simplify this, we first use the Power of a Power Rule which states: (a^m)^n = a^(m*n), therefore we can rewrite this expression as (2x^c)/(a^b*x^(4b)). Then, we separate the constants and variables to get (2/a^b) * (x^c/x^4b), subsequently you apply the division rule of exponents which says x^m/x^n = x^(m-n). So, it simplifies to (2/a^b) * x^(c-4b).
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