To rewrite the expression \( 2^{22 - 4} \) with only positive exponents, we can first simplify the exponent:
\[ 2^{22 - 4} = 2^{18} \]
Now, we need to calculate \( 2^{18} \).
Calculating \( 2^{18} \):
\[ 2^{18} = 262144 \]
Thus, the equivalent expression with only positive exponents is \( 2^{18} \), and the solution is:
\[ \boxed{262144} \]