Question

(\frac{2(n^{3})^{4}}{6n^{6}})

Explanation:

Step1: Simplify the numerator's exponent

Using the power of a power rule \((a^m)^n = a^{mn}\), for \((n^3)^4\), we have \(n^{3\times4}=n^{12}\). So the numerator becomes \(2n^{12}\).

Step2: Simplify the fraction's coefficient and exponent

First, simplify the coefficient: \(\frac{2}{6}=\frac{1}{3}\). Then, for the variable part, use the quotient rule for exponents \(\frac{a^m}{a^n}=a^{m - n}\). So \(\frac{n^{12}}{n^6}=n^{12 - 6}=n^6\).

Step3: Combine the results

Multiply the simplified coefficient and the simplified variable part: \(\frac{1}{3}\times n^6=\frac{n^6}{3}\).

Answer:

\(\frac{n^6}{3}\)