Answer:
n=9
Explanation:
Given the expression
[tex]a^3\cdot\frac{a^5}{a^{-1}}[/tex]First, we apply the subtraction law of indices (to divide powers with the same base, subtract the indices) to the quotient to obtain:
[tex]\begin{gathered} =a^3\cdot a^{5-(-1)} \\ =a^3\cdot a^{5+1} \\ =a^3\cdot a^6 \end{gathered}[/tex]Next, we apply the addition law of indices (to multiply powers with the same base, add the indices).
[tex]\begin{gathered} =a^{3+6} \\ =a^9 \end{gathered}[/tex]The value of n in a^n is therefore 9.