https://file.aiquickdraw.com/mathbot/file/1726580728741uzaxvnrq.jpg

Let's evaluate each of the expressions given in the image where \( x = 3 \):

### a. \( 2^x \)
Substituting \( x = 3 \):
\[ 2^3 = 8 \]

### b. \( 5 \cdot 2^x \)
Substituting \( x = 3 \):
\[ 5 \cdot 2^3 = 5 \cdot 8 = 40 \]

### c. \( (5 \cdot 2)^x \)
Substituting \( x = 3 \):
\[ (5 \cdot 2)^3 = 10^3 = 1000 \]

### d. \( (-x)^2 \)
Substituting \( x = 3 \):
\[ (-3)^2 = 9 \]

### e. \( (-2)^{x+1} \)
Substituting \( x = 3 \):
\[ (-2)^{3+1} = (-2)^4 = 16 \]

### f. \( -2^{x+1} \)
Substituting \( x = 3 \):
\[ -2^{3+1} = -2^4 = -16 \]

Here are the results:
- a. \( 2^3 = 8 \)
- b. \( 5 \cdot 2^3 = 40 \)
- c. \( 10^3 = 1000 \)
- d. \( 9 \)
- e. \( 16 \)
- f. \( -16 \)

If you need further details or explanations for any of these computations, feel free to ask!

**Further Questions You Might Consider:**
1. How does the base or exponent change when evaluating expressions with negative numbers?
2. What happens if \( x \) were a negative number in each of these expressions?
3. Can you explain the difference between \((-2)^{x+1}\) and \(-2^{x+1}\)?
4. How would these expressions change if \( x \) was a fraction?
5. Could you provide real-life examples where these kinds of exponential expressions might be used?

**Tip:** Always mind the order of operations, especially in expressions involving exponents and negatives. This is crucial to getting the correct result.

Evaluate each expression when x = 3: a) 2^x, b) 5 * 2^x, c) (5 * 2)^x, d) (-x)^2, e) (-2)^(x+1), f) -2^(x+1)

This guide provides step-by-step solutions to evaluate various exponential expressions with exponents, negative numbers, and order of operations when x = 3. It covers the key algebraic concepts involved in expressions such as 2^x, (-x)^2, and (-2)^(x+1). Suitable for Grades 8-10.

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