The expression you provided is:

\[
\frac{4(1 - 3^n)}{1 - 3}
\]

Let's simplify this step by step:

1. Simplify the denominator \( 1 - 3 \):
   \[
   1 - 3 = -2
   \]

2. Now substitute the result into the expression:
   \[
   \frac{4(1 - 3^n)}{-2}
   \]

3. Simplify the fraction:
   \[
   \frac{4(1 - 3^n)}{-2} = -2(1 - 3^n)
   \]

4. Finally, distribute the \(-2\):
   \[
   -2(1 - 3^n) = -2 + 2 \cdot 3^n
   \]

So, the simplified expression is:
\[
2 \cdot 3^n - 2
\]

Would you like further details or have any questions?

Here are some related questions for practice:
1. Simplify: \( \frac{5(1 - 2^n)}{1 - 2} \)
2. Simplify: \( \frac{6(1 - 4^n)}{1 - 4} \)
3. Solve for \( n \): \( 2 \cdot 3^n - 2 = 16 \)
4. Expand: \( 3 \cdot (2 - 5^n) \)
5. Factor: \( 2 \cdot 3^n - 2 \)

**Tip**: When simplifying expressions with common denominators, always simplify the denominator first to avoid unnecessary complexity.

Learn how to simplify the expression 4(1 - 3^n) / (1 - 3) with a step-by-step solution. This problem covers algebraic concepts, including simplification of expressions and handling exponents. Suitable for students in Grades 9-11.

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