Let's break down the expressions from your uploaded image. The first set of questions asks for writing expressions in exponential form.

Exponential Form Conversion:

1. x ⋅ x ⋅ x ⋅ x → This is the product of four x's, so it can be written as:
   x⁴ (Answer: E)

2. k cubed → This is simply k raised to the power of 3:
   k³ (Answer: N)

3. 12 ⋅ m ⋅ n ⋅ n → The two n's can be written as n², so the expression becomes:
   12mn² (Answer: M)

4. 1/3 ⋅ u ⋅ u ⋅ u ⋅ v ⋅ v → We have three u's and two v's, so:
   1/3 u³v² (Answer: T)

5. (a + b) ⋅ (a + b) ⋅ (a + b) → This is the product of three identical terms, so it becomes:
   (a + b)³ (Answer: E)

6. (c + d) ⋅ (c + d) ⋅ (c - d) → The first two terms are (c + d)², so the expression becomes:
   (c + d)²(c - d) (Answer: U)

7. -7 ⋅ x ⋅ (x + 3) ⋅ (x + 3) → We have two terms of (x + 3), so the expression becomes:
   -7x(x + 3)² (Answer: R)

8. (x + y) ⋅ (x + y) → This is the square of (x + y):
   (x + y)² (Answer: I)

9. the fifth power of the product of p and q → This becomes:
   (pq)⁵ (Answer: I)

Now, for the second set, we are evaluating expressions for given variable values.

Evaluating Expressions:

1. x² - 3xy if x = 5, y = 2:
   Substitute values:
   $5² - 3(5)(2) = 25 - 30 = -5$ (Answer: T)

2. x² - y² if x = -7, y = -1:
   Substitute values:
   $(-7)² - (-1)² = 49 - 1 = 48$ (Answer: H)

3. x³ if x = 2, y = -4:
   This simplifies to $2³ = 8$ (Answer: P)

4. xy² - 2x³ if x = 3, y = 2:
   Substitute values:
   $(3)(2²) - 2(3³) = 3(4) - 2(27) = 12 - 54 = -42$ (Answer: F)

5. -5a² if a = -4, b = 6:
   Substitute values:
   $-5(-4)² = -5(16) = -80$ (Answer: R)

6. 3ab² if a = 1, b = -2:
   Substitute values:
   $3(1)(-2)² = 3(1)(4) = 12$ (Answer: R)

7. (a + b)⁴ / (a²) if a = -5, b = 3:
   Substitute values:
   $((-5 + 3)⁴) / (-5)² = (-2)⁴ / 25 = 16 / 25$ (Answer: N)

Would you like to dive into more detail on any of these? Feel free to ask for further explanations!

Follow-up Questions:

1. Can you explain why we use exponents when dealing with repeated multiplication?
2. How does evaluating expressions with given values of variables help in simplifying mathematical problems?
3. What are some common properties of exponents that help with these conversions?
4. Could you explain the steps for simplifying expressions involving both addition and multiplication?
5. How do you handle more complex expressions with variables and constants?

Tip:

When simplifying expressions, always look for repeated factors that can be written in exponent form. It can make things much easier!