The problem asks us to evaluate the expression $(2^0) \cdot (\frac{2^{3 \cdot 3^3}}{2^3})$.

1. Problem Description

The problem asks us to evaluate the expression $(2^0) \cdot (\frac{2^{3 \cdot 3^3}}{2^3})$.

2. Solution Steps

First, we simplify the exponent in the numerator of the fraction.

$3^3 = 3 \cdot 3 \cdot 3 = 27$

$3 \cdot 3^3 = 3 \cdot 27 = 81$

So, the expression becomes $(2^0) \cdot (\frac{2^{81}}{2^3})$.

Next, we simplify the fraction using the rule for dividing exponents with the same base: $\frac{a^m}{a^n} = a^{m-n}$.

$\frac{2^{81}}{2^3} = 2^{81-3} = 2^{78}$

So, the expression becomes $(2^0) \cdot (2^{78})$.

Now, we simplify $2^0$. Any number raised to the power of 0 is

1.

$2^0 = 1$

The expression becomes $1 \cdot 2^{78} = 2^{78}$.

Therefore, the final answer is $2^{78}$.

3. Final Answer

$2^{78}$