https://file.aiquickdraw.com/mathbot/file/17268396265377di5022b.jpg

The image contains three mathematical expressions in Ukrainian. Let me translate and solve them:

1. \( \sqrt[3]{343} \)
2. \( \sqrt[3]{-64} \)
3. \( -\sqrt[5]{-1024} \)

### Solution:

1. **\( \sqrt[3]{343} \)**  
   The cube root of 343 is the number that, when cubed, gives 343.  
   \( 7^3 = 343 \), so  
   \[
   \sqrt[3]{343} = 7
   \]

2. **\( \sqrt[3]{-64} \)**  
   The cube root of -64 is the number that, when cubed, gives -64.  
   \( (-4)^3 = -64 \), so  
   \[
   \sqrt[3]{-64} = -4
   \]

3. **\( -\sqrt[5]{-1024} \)**  
   The fifth root of -1024 is the number that, when raised to the fifth power, gives -1024.  
   \( (-4)^5 = -1024 \), so  
   \[
   \sqrt[5]{-1024} = -4
   \]
   Therefore,  
   \[
   -\sqrt[5]{-1024} = -(-4) = 4
   \]

### Final answers:
1. \( 7 \)
2. \( -4 \)
3. \( 4 \)

Would you like more details or explanations? Here are some related questions to explore:

1. What are cube roots, and how do they relate to solving equations?
2. How can we compute cube roots and fifth roots for negative numbers?
3. What is the difference between even and odd roots for negative numbers?
4. How do you simplify expressions with higher-order roots?
5. How do cube roots apply to real-world problems?

**Tip**: Roots of negative numbers have different properties depending on whether the root is even or odd. Odd roots of negative numbers produce real results, while even roots do not in the realm of real numbers.

Чому дорівнює значення виразу: 1) ³√343; 2) ³√-64; 3) -⁵√-1024?

Learn how to compute cube and fifth roots with examples like ³√343, ³√-64, and -⁵√-1024. These exercises cover the mathematical properties of roots and negative numbers. Suitable for students in Grades 8-10.

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