https://file.aiquickdraw.com/mathbot/file/17256178138129wtyv7hd.jpg

I have reviewed the image of your math problems. I'll begin solving them step by step. Here are the questions presented in the image:

1. **Simplify the following expressions** (multiple choices A to D).
2. **Substitute values into an expression**.
3. **Identify which equation is true** (multiple choices A to E).
4. **Simplify a given expression**.
5. **Find the final exponent of an expression involving \(x\)**.
6. **Simplify the expression** \( \sqrt{6 \cdot 27} \) and similar square root operations.
7. **Evaluate an equation** involving square roots.
8. **Resolve the final expression** \( E = \left( \frac{81^{\frac{3}{4}}}{27^{\frac{5}{6}}} \right)^{\frac{1}{2}} \).

I'll now start solving each one individually.

### Problem 1: Simplifying Expressions
I'll begin by simplifying each expression.Here are the simplified results for each expression in Problem 1:

- **A**: \(-216\sqrt{2} + 270\sqrt{10}\)
- **B**: \(2\sqrt{30}\)
- **C**: \(7\sqrt{3}\)
- **D**: \(14\sqrt{5}\)

Let's proceed to Problem 2, which involves substituting values into the expression.For **Problem 2**, after substituting \( x = 5 \), the result is:

\[ 150\sqrt{5} \]

Next, I'll work on **Problem 3**, which asks to determine which equation is true.It seems like I can’t do more advanced data analysis right now. Please try again later. Would you like me to continue solving the problems manually, or perhaps try another approach?

Feel free to ask any questions, and here are a few to consider:
1. Would you like to explore the detailed steps for the earlier simplifications?
2. Do you need help with a specific math topic related to these problems?
3. Do you want more examples of exponent or root calculations?
4. Should I attempt to provide explanations for other exercises from the image?
5. Are there any formulas you'd like to explore in detail?

**Tip**: Always double-check your answers by substituting them back into the original equation when possible!

This webpage walks through solving various math problems that involve simplifying expressions, evaluating exponents and roots, and performing substitutions. Key topics include exponent rules, square root operations, and expression simplification, suitable for students in Grades 10-12.

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