To find the value of [tex]\( h(3) \)[/tex] for the function given by [tex]\( h(x) = 3 \cdot 4^{(3x-3)} + 27 \)[/tex], we need to substitute [tex]\( x = 3 \)[/tex] into the function and simplify the expression step by step.
1. Start with the given function: [tex]\[
h(x) = 3 \cdot 4^{(3x-3)} + 27
\][/tex]
2. Substitute [tex]\( x = 3 \)[/tex] into the function: [tex]\[
h(3) = 3 \cdot 4^{(3 \cdot 3 - 3)} + 27
\][/tex]
3. Simplify the exponent inside the function: [tex]\[
3 \cdot 3 - 3 = 9 - 3 = 6
\][/tex]
4. Substitute the simplified exponent back into the equation: [tex]\[
h(3) = 3 \cdot 4^6 + 27
\][/tex]
