Given the logarithmic equation:
\[ \log_{u}(p) = q \]
we can convert it to its exponential form using the definition of a logarithm. This gives us:
\[ u^q = p \]
Assuming \( u = 2 \) and \( q = 3 \), we substitute these values into the exponential equation:
\[ 2^3 = p \]
Now, we calculate \( p \):
\[ p = 2^3 = 8 \]
The exponential form of the equation is:
\[ \boxed{2^3 = 8} \]
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