Question

1. \\((n^2n^4)^{-4}\\)

Explanation:

Step1: Combine exponents inside the parentheses

When multiplying exponents with the same base, we add the exponents. So \( n^2 \cdot n^4 = n^{2 + 4}=n^6 \).

Step2: Apply the power of a power rule

The power of a power rule states that \( (a^m)^n=a^{m\times n} \). Here, \( a = n \), \( m = 6 \), and \( n=- 4 \). So \( (n^6)^{-4}=n^{6\times(-4)}=n^{-24} \).

Step3: Convert negative exponent to positive (optional, but common)

Recall that \( a^{-m}=\frac{1}{a^m} \), so \( n^{-24}=\frac{1}{n^{24}} \).

Answer:

\(\frac{1}{n^{24}}\) (or \(n^{-24}\))