Exponents Practice Worksheet 2-4

Let's go through each problem step by step and solve them.

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Write using exponents.

We rewrite repeated multiplication using exponent notation:
Base^Exponent, where the base is the number being multiplied, and the exponent is how many times it's multiplied.

1. $ 3 \times 3 \times 3 \times 3 $
→ Four 3s → $ 3^4 $

2. $ 364 \times 364 $
→ Two 364s → $ 364^2 $

3. $ 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 $
→ Seven 2s → $ 2^7 $

4. $ 13 \times 13 \times 13 $
→ Three 13s → $ 13^3 $

5. $ 8 \times 8 \times 8 \times 7 \times 7 $
→ Three 8s and two 7s → $ 8^3 \times 7^2 $

6. $ 49 $
→ 49 is $ 7 \times 7 $ → $ 7^2 $

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Write in expanded form.

Expanded form means writing out the multiplication.

7. $ 10^4 $ → $ 10 \times 10 \times 10 \times 10 $

8. $ 6^5 $ → $ 6 \times 6 \times 6 \times 6 \times 6 $

9. $ 3^2 $ → $ 3 \times 3 $

10. $ 7^3 $ → $ 7 \times 7 \times 7 $

11. $ 12^4 $ → $ 12 \times 12 \times 12 \times 12 $

12. "5 cubed" → $ 5^3 $ → $ 5 \times 5 \times 5 $

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Write in standard form.

Standard form means evaluate the expression.

13. $ 5^4 = 5 \times 5 \times 5 \times 5 = 625 $

14. $ 2^6 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 = 64 $

15. "11 squared" = $ 11^2 = 11 \times 11 = 121 $

16. $ 10^7 = 10,000,000 $ (1 followed by 7 zeros)

17. $ 12^2 = 12 \times 12 = 144 $

18. "6 cubed" = $ 6^3 = 6 \times 6 \times 6 = 216 $

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Compare using <, >, or =

We evaluate both sides and compare.

19. $ 4^2 \bigcirc 2^4 $
$ 4^2 = 16 $, $ 2^4 = 16 $ → $ 16 = 16 $ → =

20. $ 4^3 \bigcirc 3^4 $
$ 4^3 = 64 $, $ 3^4 = 81 $ → $ 64 < 81 $ → <

21. $ 5^8 \bigcirc 5^9 $
Same base, higher exponent → $ 5^8 < 5^9 $ → <

22. $ 3^8 \bigcirc 3 \times 8 $
$ 3^8 = 6561 $, $ 3 \times 8 = 24 $ → $ 6561 > 24 $ → >

23. $ 2^5 \bigcirc 5^2 $
$ 2^5 = 32 $, $ 5^2 = 25 $ → $ 32 > 25 $ → >

24. $ 10^3 \bigcirc 10 + 10 + 10 $
$ 10^3 = 1000 $, $ 10+10+10 = 30 $ → $ 1000 > 30 $ → >

25. $ 5^3 \bigcirc 5 \times 5 \times 5 $
$ 5^3 = 125 $, $ 5 \times 5 \times 5 = 125 $ → =

26. $ 7^3 \bigcirc 3^7 $
$ 7^3 = 343 $, $ 3^7 = 2187 $ → $ 343 < 2187 $ → <

27. $ 10^4 \bigcirc 4 \times 10 $
$ 10^4 = 10,000 $, $ 4 \times 10 = 40 $ → $ 10,000 > 40 $ → >

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Final Answers:

#### Write using exponents
1. $ 3^4 $
2. $ 364^2 $
3. $ 2^7 $
4. $ 13^3 $
5. $ 8^3 \times 7^2 $
6. $ 7^2 $

#### Write in expanded form
7. $ 10 \times 10 \times 10 \times 10 $
8. $ 6 \times 6 \times 6 \times 6 \times 6 $
9. $ 3 \times 3 $
10. $ 7 \times 7 \times 7 $
11. $ 12 \times 12 \times 12 \times 12 $
12. $ 5 \times 5 \times 5 $

#### Write in standard form
13. 625
14. 64
15. 121
16. 10,000,000
17. 144
18. 216

#### Compare
19. =
20. <
21. <
22. >
23. >
24. >
25. =
26. <
27. >

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✔ All problems are solved! Let me know if you'd like this formatted as a printable answer sheet.