https://file.aiquickdraw.com/mathbot/file/1725874351499h6q2156d.jpg

I can see the worksheet you've uploaded. Let's focus on simplifying the expressions and solving the equation in the image. 

### 1. Classification of Sets:
The sets listed here seem to refer to different categories of numbers:
- Real Numbers (a)
- Natural Numbers (b)
- Whole Numbers (c)
- Integers (d)
- Irrational Numbers (e)

### 2. Simplifying the Expressions:
Here are the expressions under section 3 that need simplification:

**a.** \( \left( \frac{-7a^2 b^3 c^0}{3a^3 b^4 c^3} \right)^{-4} \)

We can simplify this step by step:
1. Start by simplifying the inside:
   \[ \frac{-7a^2 b^3 c^0}{3a^3 b^4 c^3} = \frac{-7 b^3}{3 a b^4 c^3} = \frac{-7}{3a b c^3} \]
   
2. Now apply the power of \(-4\):
   \[
   \left( \frac{-7}{3a b c^3} \right)^{-4} = \left( \frac{3 a b c^3}{-7} \right)^4 = \frac{(3^4) (a^4) (b^4) (c^{12})}{(-7)^4}
   \]

Final simplified form:
\[ \frac{81 a^4 b^4 c^{12}}{2401} \]

Would you like help with the other expressions or solving the equation?

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Here are some related questions to further your understanding:

1. How do we simplify expressions with negative exponents?
2. What are the properties of exponents applied to fractions?
3. What is the difference between real numbers and irrational numbers?
4. How do you solve exponential equations such as \(42^x = 1024\)?
5. How does the behavior of radicals change when combined with different powers?

**Tip**: Always simplify the inside of an expression before applying an exponent or root. This helps to avoid errors when working with complex terms.

Simplify the given expressions and solve for x in the provided equations.

Explore step-by-step solutions to simplify expressions using exponents and radicals, and solve algebraic equations for x. This worksheet is suitable for students in Grades 9-11, covering key algebraic concepts such as negative exponents, laws of exponents, and quadratic equation solving.

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