Question

simplify. express your answer using positive expon\\(\frac{n^{-3}}{n^{9}\cdot n^{4}}\\)

Explanation:

Step1: Simplify the denominator using exponent rule \(a^m \cdot a^n = a^{m + n}\)

The denominator is \(n^9 \cdot n^4\), so applying the rule, we get \(n^{9 + 4}=n^{13}\). Now the expression becomes \(\frac{n^{-3}}{n^{13}}\).

Step2: Use the exponent rule \(\frac{a^m}{a^n}=a^{m - n}\)

Applying this rule to \(\frac{n^{-3}}{n^{13}}\), we have \(n^{-3-13}=n^{-16}\).

Step3: Convert negative exponent to positive using \(a^{-n}=\frac{1}{a^n}\)

So \(n^{-16}=\frac{1}{n^{16}}\).

Answer:

\(\frac{1}{n^{16}}\)