To simplify the expression \( 13^6 \cdot 13^{-1/2} \), we can use the properties of exponents.
We can combine the exponents since they have the same base:
\[ 13^6 \cdot 13^{-1/2} = 13^{6 + (-1/2)} = 13^{6 - 1/2} \]
Now, we can convert \( 6 \) to a fraction to facilitate the subtraction:
\[ 6 = \frac{12}{2} \]
So, we have:
\[ 6 - \frac{1}{2} = \frac{12}{2} - \frac{1}{2} = \frac{12 - 1}{2} = \frac{11}{2} \]
Thus, the expression simplifies to:
\[ 13^{\frac{11}{2}} \]
Therefore, the equivalent expression is:
\[ 13^{\frac{11}{2}} \]