Let's break down and simplify the given equation step by step:
1. Initial Equation:
[tex]\[
72 \cdot m \cdot n \cdot n \cdot m \cdot 4^{a \cdot b \cdot c} = 11 + 5
\][/tex]
2. Simplify the Right Hand Side (RHS):
[tex]\[
11 + 5 = 16
\][/tex]
3. Rewrite the Left Hand Side (LHS):
Since we have [tex]\( m \)[/tex] and [tex]\( n \)[/tex] appearing twice, we can combine like terms:
[tex]\[
72 \cdot m \cdot m \cdot n \cdot n \cdot 4^{a \cdot b \cdot c} = 72 \cdot m^2 \cdot n^2 \cdot 4^{a \cdot b \cdot c}
\][/tex]
4. Substitute back into the equation:
[tex]\[
72 \cdot m^2 \cdot n^2 \cdot 4^{a \cdot b \cdot c} = 16
\][/tex]
5. Analysis:
At this stage, we need values for [tex]\( m \)[/tex], [tex]\( n \)[/tex], [tex]\( a \)[/tex], [tex]\( b \)[/tex], and [tex]\( c \)[/tex] to proceed further. However, since these variables are unspecified, we cannot find numerical solutions or simplify the equation any further with the information given.
In conclusion, without specific values for [tex]\( m \)[/tex], [tex]\( n \)[/tex], [tex]\( a \)[/tex], [tex]\( b \)[/tex], and [tex]\( c \)[/tex], the equation cannot be solved further. The variables must be known to find a unique solution.
