Exponent practice worksheet for students to calculate and compare powers.

Problem: Solving Exponents and Ordering Them

#### Step 1: Solve the Basic Exponent Problems
We are given several exponent problems to solve. Let's work through each one step by step.

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Part 1: Basic Exponent Calculations

#### Example Problems:
- \( 5^2 = 5 \times 5 = 25 \)
- \( 2^4 = 2 \times 2 \times 2 \times 2 = 16 \)
- \( 10^3 = 10 \times 10 \times 10 = 1000 \)

#### Problems to Solve:
1. \( 3^2 = 3 \times 3 = 9 \)
2. \( 2^3 = 2 \times 2 \times 2 = 8 \)
3. \( 6^2 = 6 \times 6 = 36 \)
4. \( 9^2 = 9 \times 9 = 81 \)
5. \( 3^3 = 3 \times 3 \times 3 = 27 \)
6. \( 7^2 = 7 \times 7 = 49 \)

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Part 2: Use a Calculator for Larger Exponents

#### Problems to Solve:
7. \( 4^3 = 4 \times 4 \times 4 = 64 \)
8. \( 2^5 = 2 \times 2 \times 2 \times 2 \times 2 = 32 \)
9. \( 5^4 = 5 \times 5 \times 5 \times 5 = 625 \)
10. \( 9^3 = 9 \times 9 \times 9 = 729 \)
11. \( 3^5 = 3 \times 3 \times 3 \times 3 \times 3 = 243 \)
12. \( 7^4 = 7 \times 7 \times 7 \times 7 = 2401 \)
13. \( 10^5 = 10 \times 10 \times 10 \times 10 \times 10 = 100,000 \)
14. \( 2^7 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 = 128 \)
15. \( 9^5 = 9 \times 9 \times 9 \times 9 \times 9 = 59,049 \)
16. \( 16^3 = 16 \times 16 \times 16 = 4096 \)
17. \( 6^1 = 6 \)
18. \( 5^6 = 5 \times 5 \times 5 \times 5 \times 5 \times 5 = 15,625 \)
19. \( 78^2 = 78 \times 78 = 6084 \)

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Part 3: Order the Exponents from Smallest to Largest

We are given the following exponents to order:
- \( 5^6 \)
- \( 2^9 \)
- \( 6^4 \)
- \( 9^3 \)
- \( 10^4 \)
- \( 7^5 \)

#### Step-by-Step Calculation:
1. \( 5^6 \):
\[
5^6 = 5 \times 5 \times 5 \times 5 \times 5 \times 5 = 15,625
\]

2. \( 2^9 \):
\[
2^9 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 = 512
\]

3. \( 6^4 \):
\[
6^4 = 6 \times 6 \times 6 \times 6 = 1296
\]

4. \( 9^3 \):
\[
9^3 = 9 \times 9 \times 9 = 729
\]

5. \( 10^4 \):
\[
10^4 = 10 \times 10 \times 10 \times 10 = 10,000
\]

6. \( 7^5 \):
\[
7^5 = 7 \times 7 \times 7 \times 7 \times 7 = 16,807
\]

#### Ordering the Results:
Now, we compare the values:
- \( 2^9 = 512 \)
- \( 9^3 = 729 \)
- \( 6^4 = 1296 \)
- \( 5^6 = 15,625 \)
- \( 10^4 = 10,000 \)
- \( 7^5 = 16,807 \)

Ordering them from smallest to largest:
\[
2^9, \, 9^3, \, 6^4, \, 10^4, \, 5^6, \, 7^5
\]

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Final Answer:

\[
\boxed{2^9, \, 9^3, \, 6^4, \, 10^4, \, 5^6, \, 7^5}
\]