Math worksheet for practicing exponents and roots with problems and examples.

Problem Analysis:

The worksheet consists of three sections:
1. Section A: Calculating powers (e.g., \(2^2\), \(3^2\), etc.).
2. Section B: Calculating square roots (e.g., \(\sqrt{16}\), \(\sqrt{25}\), etc.).
3. Section C: Calculating cube roots (e.g., \(\sqrt[3]{8}\), \(\sqrt[3]{27}\), etc.).

We will solve each section step by step.

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Section A: Powers

#### 1. \(2^2 = 2 \times 2 = 4\)
- Given in the problem.

#### 2. \(2^4\)
- \(2^4 = 2 \times 2 \times 2 \times 2 = 16\)

#### 3. \(3^2\)
- \(3^2 = 3 \times 3 = 9\)

#### 4. \(4^3\)
- \(4^3 = 4 \times 4 \times 4 = 64\)

#### 5. \(5^2\)
- \(5^2 = 5 \times 5 = 25\)

#### 6. \(10^3\)
- \(10^3 = 10 \times 10 \times 10 = 1000\)

#### 7. \(12^2\)
- \(12^2 = 12 \times 12 = 144\)

#### 8. \(8^3\)
- \(8^3 = 8 \times 8 \times 8 = 512\)

#### 9. \(7^2\)
- \(7^2 = 7 \times 7 = 49\)

#### 10. \(4^3\)
- \(4^3 = 4 \times 4 \times 4 = 64\)

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Section B: Square Roots

#### 11. \(\sqrt{16}\)
- \(\sqrt{16} = 4\) because \(4 \times 4 = 16\).

#### 12. \(\sqrt{25}\)
- \(\sqrt{25} = 5\) because \(5 \times 5 = 25\).

#### 13. \(\sqrt{100}\)
- \(\sqrt{100} = 10\) because \(10 \times 10 = 100\).

#### 14. \(\sqrt{81}\)
- \(\sqrt{81} = 9\) because \(9 \times 9 = 81\).

#### 15. \(\sqrt{144}\)
- \(\sqrt{144} = 12\) because \(12 \times 12 = 144\).

#### 16. \(\sqrt{1600}\)
- \(\sqrt{1600} = 40\) because \(40 \times 40 = 1600\).

#### 17. \(\sqrt{8100}\)
- \(\sqrt{8100} = 90\) because \(90 \times 90 = 8100\).

#### 18. \(\sqrt{49}\)
- \(\sqrt{49} = 7\) because \(7 \times 7 = 49\).

#### 19. \(\sqrt{121}\)
- \(\sqrt{121} = 11\) because \(11 \times 11 = 121\).

#### 20. \(\sqrt{64}\)
- \(\sqrt{64} = 8\) because \(8 \times 8 = 64\).

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Section C: Cube Roots

#### 21. \(\sqrt[3]{8}\)
- \(\sqrt[3]{8} = 2\) because \(2 \times 2 \times 2 = 8\).

#### 22. \(\sqrt[3]{27}\)
- \(\sqrt[3]{27} = 3\) because \(3 \times 3 \times 3 = 27\).

#### 23. \(\sqrt[3]{125}\)
- \(\sqrt[3]{125} = 5\) because \(5 \times 5 \times 5 = 125\).

#### 24. \(\sqrt[3]{1000}\)
- \(\sqrt[3]{1000} = 10\) because \(10 \times 10 \times 10 = 1000\).

#### 25. \(\sqrt[3]{512}\)
- \(\sqrt[3]{512} = 8\) because \(8 \times 8 \times 8 = 512\).

#### 26. \(\sqrt[3]{125}\)
- \(\sqrt[3]{125} = 5\) because \(5 \times 5 \times 5 = 125\).

#### 27. \(\sqrt[3]{64}\)
- \(\sqrt[3]{64} = 4\) because \(4 \times 4 \times 4 = 64\).

#### 28. \(\sqrt[3]{343}\)
- \(\sqrt[3]{343} = 7\) because \(7 \times 7 \times 7 = 343\).

#### 29. \(\sqrt[3]{729}\)
- \(\sqrt[3]{729} = 9\) because \(9 \times 9 \times 9 = 729\).

#### 30. \(\sqrt[3]{216}\)
- \(\sqrt[3]{216} = 6\) because \(6 \times 6 \times 6 = 216\).

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Final Answers:

\[
\boxed{
\begin{array}{ll}
\text{A.} & 2, 16, 9, 64, 25, 1000, 144, 512, 49, 64 \\
\text{B.} & 4, 5, 10, 9, 12, 40, 90, 7, 11, 8 \\
\text{C.} & 2, 3, 5, 10, 8, 5, 4, 7, 9, 6 \\
\end{array}
}
\]