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.