https://file.aiquickdraw.com/mathbot/file/1729580812980l1j14y2i.jpg

Let's go through each of the problems in the image where \( s = 4 \) and \( t = 8 \).

### 25. \( (s + t)^3 \)
Substitute \( s = 4 \) and \( t = 8 \):
\[
(4 + 8)^3 = 12^3 = 1728
\]

### 26. \( s^4 + t^2 + s \div 2 \)
Substitute \( s = 4 \) and \( t = 8 \):
\[
4^4 + 8^2 + \frac{4}{2} = 256 + 64 + 2 = 322
\]

### 27. \( \frac{(st)^2}{(st^2)} \)
Substitute \( s = 4 \) and \( t = 8 \):
\[
\frac{(4 \times 8)^2}{(4 \times 8^2)} = \frac{32^2}{4 \times 64} = \frac{1024}{256} = 4
\]

### 28. \( 3st^2 \div (st) + 6 \)
Substitute \( s = 4 \) and \( t = 8 \):
\[
\frac{3 \times 4 \times 8^2}{4 \times 8} + 6 = \frac{3 \times 4 \times 64}{32} + 6 = \frac{768}{32} + 6 = 24 + 6 = 30
\]

### 29. \( (t - s)^5 \)
Substitute \( s = 4 \) and \( t = 8 \):
\[
(8 - 4)^5 = 4^5 = 1024
\]

### 30. \( (2s)^2t \)
Substitute \( s = 4 \) and \( t = 8 \):
\[
(2 \times 4)^2 \times 8 = 8^2 \times 8 = 64 \times 8 = 512
\]

### 31. \( 2st^2 - s^2 \)
Substitute \( s = 4 \) and \( t = 8 \):
\[
2 \times 4 \times 8^2 - 4^2 = 2 \times 4 \times 64 - 16 = 512 - 16 = 496
\]

### 32. \( 2s^2 - \frac{t^3}{16} \)
Substitute \( s = 4 \) and \( t = 8 \):
\[
2 \times 4^2 - \frac{8^3}{16} = 2 \times 16 - \frac{512}{16} = 32 - 32 = 0
\]

### 33. \( \frac{(3s)^3t + t}{s} \)
Substitute \( s = 4 \) and \( t = 8 \):
\[
\frac{(3 \times 4)^3 \times 8 + 8}{4} = \frac{12^3 \times 8 + 8}{4} = \frac{1728 \times 8 + 8}{4} = \frac{13824 + 8}{4} = \frac{13832}{4} = 3458
\]

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Do you have any questions, or would you like more detailed explanations for any of the steps?

Here are 5 related questions you can explore:
1. How would you simplify the expression \( (2s)^3 \times t^2 \) for given values of \( s \) and \( t \)?
2. What happens when you switch the values of \( s \) and \( t \) in these problems?
3. How would you solve \( (st)^n - s^n \) for \( s = 4 \), \( t = 8 \), and \( n = 3 \)?
4. What is the general form of a polynomial expression for \( s = 4 \) and \( t = 8 \)?
5. How would you evaluate \( (s + t)^4 - (s - t)^2 \)?

**Tip:** When evaluating large exponents like \( a^3 \), try breaking them into smaller multiplications for quicker mental calculations.

Evaluate each expression for s = 4 and t = 8.

Learn how to evaluate expressions such as (s + t)^3 and 2st^2 - s^2 for given values of s and t. This guide uses substitution and algebraic manipulation to solve expressions, suitable for students in Grades 7-9.

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