Question

n^\frac{4}{5} \cdot n^\frac{2}{5}

Explanation:

Step1: Apply exponent product rule

When multiplying two exponential expressions with the same base, we add the exponents. The rule is \(a^m \cdot a^n = a^{m + n}\). Here, the base is \(n\), \(m=\frac{4}{5}\), and \(n = \frac{2}{5}\). So we have \(n^{\frac{4}{5}} \cdot n^{\frac{2}{5}}=n^{\frac{4}{5}+\frac{2}{5}}\).

Step2: Add the exponents

Calculate \(\frac{4}{5}+\frac{2}{5}\). Since the denominators are the same, we add the numerators: \(\frac{4 + 2}{5}=\frac{6}{5}\). So the expression simplifies to \(n^{\frac{6}{5}}\).

Answer:

\(n^{\frac{6}{5}}\)