Simplify : 2^ \ 3x-2[4(x-2)+1]\ -x; - 11x + 28; - 9x + 4; - 10x + 28; - 11x + 20; 8x + 28

Let's simplify the expression step by step:

### Expression:
\[ 2^{3x} - 2[4(x - 2) + 1] - x \]

### Step 1: Simplify inside the brackets
Inside the brackets, we have:
\[ 4(x - 2) + 1 \]

Distribute \( 4 \) to \( x - 2 \):
\[ 4(x - 2) = 4x - 8 \]

Now, add 1:
\[ 4x - 8 + 1 = 4x - 7 \]

### Step 2: Multiply by -2
Now multiply \( -2 \) by \( (4x - 7) \):
\[ -2(4x - 7) = -8x + 14 \]

### Step 3: Substitute and simplify
Now we substitute this back into the original expression:
\[ 2^{3x} - (8x - 14) - x \]

Simplify the terms:
\[ 2^{3x} - 8x + 14 - x \]

Combine like terms:
\[ 2^{3x} - 9x + 14 \]

### Final Simplified Expression:
\[
2^{3x} - 9x + 14
\]

Let me know if you'd like more details, or if you have any questions!

Here are five related questions:
1. How would you solve \( 2^{3x} - 9x + 14 = 0 \)?
2. Can you apply logarithmic rules to solve an equation involving \( 2^{3x} \)?
3. How does the distributive property apply to simplifying algebraic expressions?
4. What is the importance of combining like terms in algebraic simplification?
5. How does exponentiation affect the growth of a function compared to linear terms?

**Tip**: Always simplify expressions inside parentheses or brackets first before applying other operations.

This step-by-step guide simplifies an algebraic expression involving exponentiation and distribution: 2^3x - 2[4(x-2) + 1] - x. Learn to apply the distributive property and combine like terms. Suitable for students in Grades 9-12.

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