Comparing Exponents Worksheet - Students compare exponential expressions and select the correct symbol.

To solve this worksheet, we need to compare the values of exponential expressions. Let's go through each problem step by step.

Problem 1: \(4^4\) vs \(4^2\)

- \(4^4 = 4 \times 4 \times 4 \times 4 = 256\)
- \(4^2 = 4 \times 4 = 16\)
- Since \(256 > 16\), the answer is \(>\).

Problem 2: \(15^3\) vs \(15^2\)

- \(15^3 = 15 \times 15 \times 15 = 3375\)
- \(15^2 = 15 \times 15 = 225\)
- Since \(3375 > 225\), the answer is \(>\).

Problem 3: \(2^2\) vs \(5^2\)

- \(2^2 = 2 \times 2 = 4\)
- \(5^2 = 5 \times 5 = 25\)
- Since \(4 < 25\), the answer is \(<\).

Problem 4: \(9^2\) vs \(3^2\)

- \(9^2 = 9 \times 9 = 81\)
- \(3^2 = 3 \times 3 = 9\)
- Since \(81 > 9\), the answer is \(>\).

Problem 5: \(10^3\) vs \(9^3\)

- \(10^3 = 10 \times 10 \times 10 = 1000\)
- \(9^3 = 9 \times 9 \times 9 = 729\)
- Since \(1000 > 729\), the answer is \(>\).

Problem 6: \(2^{10}\) vs \(4^8\)

- \(2^{10} = 1024\)
- \(4^8 = (2^2)^8 = 2^{16} = 65536\)
- Since \(1024 < 65536\), the answer is \(<\).

Problem 7: \(7^3\) vs \(14^2\)

- \(7^3 = 7 \times 7 \times 7 = 343\)
- \(14^2 = 14 \times 14 = 196\)
- Since \(343 > 196\), the answer is \(>\).

Problem 8: \(2^8\) vs \(3^5\)

- \(2^8 = 256\)
- \(3^5 = 3 \times 3 \times 3 \times 3 \times 3 = 243\)
- Since \(256 > 243\), the answer is \(>\).

Problem 9: \(12^1\) vs \(13^0\)

- \(12^1 = 12\)
- \(13^0 = 1\)
- Since \(12 > 1\), the answer is \(>\).

Problem 10: \(25\) vs \(5^2\)

- \(25 = 25\)
- \(5^2 = 5 \times 5 = 25\)
- Since \(25 = 25\), the answer is \(=\).

Problem 11: \(12^2\) vs \(21^2\)

- \(12^2 = 12 \times 12 = 144\)
- \(21^2 = 21 \times 21 = 441\)
- Since \(144 < 441\), the answer is \(<\).

Problem 12: \(6^2\) vs \(12^1\)

- \(6^2 = 6 \times 6 = 36\)
- \(12^1 = 12\)
- Since \(36 > 12\), the answer is \(>\).

Problem 13: \(20^3\) vs \(40^1\)

- \(20^3 = 20 \times 20 \times 20 = 8000\)
- \(40^1 = 40\)
- Since \(8000 > 40\), the answer is \(>\).

Problem 14: \(9^6\) vs \(10^4\)

- \(9^6 = 531441\)
- \(10^4 = 10000\)
- Since \(531441 > 10000\), the answer is \(>\).

Problem 15: \(2^0\) vs \(4^0\)

- \(2^0 = 1\)
- \(4^0 = 1\)
- Since \(1 = 1\), the answer is \(=\).

Problem 16: \(11^6\) vs \(2^8\)

- \(11^6 = 1771561\)
- \(2^8 = 256\)
- Since \(1771561 > 256\), the answer is \(>\).

Problem 17: \(104^8\) vs \(10^9\)

- \(104^8\) is a very large number.
- \(10^9 = 1000000000\)
- Since \(104^8\) is much larger than \(10^9\), the answer is \(>\).

Problem 18: \(10^{10}\) vs \(12^{12}\)

- \(10^{10} = 10000000000\)
- \(12^{12}\) is a very large number.
- Since \(12^{12}\) is larger than \(10^{10}\), the answer is \(<\).

Problem 19: \(8^2\) vs \(6^2\)

- \(8^2 = 8 \times 8 = 64\)
- \(6^2 = 6 \times 6 = 36\)
- Since \(64 > 36\), the answer is \(>\).

Problem 20: \(6^3\) vs \(8^{13}\)

- \(6^3 = 6 \times 6 \times 6 = 216\)
- \(8^{13}\) is a very large number.
- Since \(8^{13}\) is much larger than \(216\), the answer is \(<\).

Problem 21: \(5^7\) vs \(7^5\)

- \(5^7 = 78125\)
- \(7^5 = 16807\)
- Since \(78125 > 16807\), the answer is \(>\).

Final Answer:
1. >
2. >
3. <
4. >
5. >
6. <
7. >
8. >
9. >
10. =
11. <
12. >
13. >
14. >
15. =
16. >
17. >
18. <
19. >
20. <
21. >