To simplify the expression \( 13^6 \cdot 13^{-1/2} \), you can use the property of exponents that states \( a^m \cdot a^n = a^{m+n} \).
So, in this case, we add the exponents:
\[ 13^6 \cdot 13^{-1/2} = 13^{6 + (-1/2)} = 13^{6 - 1/2} = 13^{6 - 0.5} = 13^{5.5} \]
Therefore, the equivalent expression is:
\[ 13^{5.5} \]
Alternatively, it can also be expressed as:
\[ 13^{11/2} \]
Both forms, \( 13^{5.5} \) and \( 13^{11/2} \), are equivalent.