This worksheet provides a structured way for students to practice calculating powers, square roots, and cube roots.

Let's solve each part of the problem step by step.

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A. Find the answer, show your working

We are calculating powers (exponents).

1) $ 2^2 = 2 \times 2 = 4 $ ✔ (Given)

2) $ 2^4 = 2 \times 2 \times 2 \times 2 = 16 $

3) $ 3^2 = 3 \times 3 = 9 $

4) $ 4^3 = 4 \times 4 \times 4 = 64 $

5) $ 5^2 = 5 \times 5 = 25 $

6) $ 10^3 = 10 \times 10 \times 10 = 1000 $

7) $ 12^2 = 12 \times 12 = 144 $

8) $ 8^3 = 8 \times 8 \times 8 = 512 $

9) $ 7^2 = 7 \times 7 = 49 $

10) $ 4^3 = 4 \times 4 \times 4 = 64 $

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B. Find the answer

These are square roots ($\sqrt{}$ means square root, i.e., $ \sqrt{x} = y $ if $ y^2 = x $)

11) $ \sqrt{16} = 4 $ ✔ (Given)

12) $ \sqrt{25} = 5 $ because $ 5^2 = 25 $

13) $ \sqrt{100} = 10 $ because $ 10^2 = 100 $

14) $ \sqrt{81} = 9 $ because $ 9^2 = 81 $

15) $ \sqrt{144} = 12 $ because $ 12^2 = 144 $

16) $ \sqrt{1600} = 40 $ because $ 40^2 = 1600 $

17) $ \sqrt{8100} = 90 $ because $ 90^2 = 8100 $

18) $ \sqrt{49} = 7 $ because $ 7^2 = 49 $

19) $ \sqrt{121} = 11 $ because $ 11^2 = 121 $

20) $ \sqrt{64} = 8 $ because $ 8^2 = 64 $

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C. Find the answer

These are cube roots ($ \sqrt[3]{x} $ means a number that when multiplied by itself three times gives $ x $)

21) $ \sqrt[3]{8} = 2 $ because $ 2^3 = 8 $

22) $ \sqrt[3]{27} = 3 $ because $ 3^3 = 27 $

23) $ \sqrt[3]{125} = 5 $ because $ 5^3 = 125 $

24) $ \sqrt[3]{1000} = 10 $ because $ 10^3 = 1000 $

25) $ \sqrt[3]{512} = 8 $ because $ 8^3 = 512 $

26) $ \sqrt[3]{125} = 5 $ (same as #23)

27) $ \sqrt[3]{64} = 4 $ because $ 4^3 = 64 $

28) $ \sqrt[3]{343} = 7 $ because $ 7^3 = 343 $

29) $ \sqrt[3]{729} = 9 $ because $ 9^3 = 729 $

30) $ \sqrt[3]{216} = 6 $ because $ 6^3 = 216 $

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✔ Final Answers:

#### A.
1) 4
2) 16
3) 9
4) 64
5) 25
6) 1000
7) 144
8) 512
9) 49
10) 64

#### B.
11) 4
12) 5
13) 10
14) 9
15) 12
16) 40
17) 90
18) 7
19) 11
20) 8

#### C.
21) 2
22) 3
23) 5
24) 10
25) 8
26) 5
27) 4
28) 7
29) 9
30) 6

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🔍 Explanation Summary:

- Exponentiation: $ a^n $ means multiplying $ a $ by itself $ n $ times.
- Square root: $ \sqrt{x} $ is the number that, when squared, gives $ x $. Only positive values are considered here (principal root).
- Cube root: $ \sqrt[3]{x} $ is the number that, when cubed, gives $ x $.

All answers are based on memorizing common squares and cubes or simple multiplication checks.

Let me know if you'd like this in a printable format!