Grade 5 Math worksheets 596 pages - Free Printable

I'll solve this exponent worksheet step by step, working through each problem carefully.

Let me start with the basic exponents (problems 1-9):

Problem 1: 2³ = 2 × 2 × 2 = 8

Problem 2: 4² = 4 × 4 = 16

Problem 3: 5¹ = 5 (any number to the power of 1 is itself)

Problem 4: 10² = 10 × 10 = 100

Problem 5: 8² = 8 × 8 = 64

Problem 6: 1⁴ = 1 × 1 × 1 × 1 = 1 (1 to any power is always 1)

Problem 7: 3³ = 3 × 3 × 3 = 27

Problem 8: 10³ = 10 × 10 × 10 = 1000

Problem 9: 2⁴ = 2 × 2 × 2 × 2 = 16

Now for problems 10-15 (exponent subtraction and addition):

Problem 10: 3² - 2³
- 3² = 9
- 2³ = 8
- 9 - 8 = 1

Problem 11: 5² + 3²
- 5² = 25
- 3² = 9
- 25 + 9 = 34

Problem 12: 10² - 7²
- 10² = 100
- 7² = 49
- 100 - 49 = 51

Problem 13: 3³ + 6²
- 3³ = 27
- 6² = 36
- 27 + 36 = 63

Problem 14: 2⁴ - 4²
- 2⁴ = 16
- 4² = 16
- 16 - 16 = 0

Problem 15: 9² - 8²
- 9² = 81
- 8² = 64
- 81 - 64 = 17

Now for problems 16-19 (using calculator):

Problem 16: 5² × 3³
- 5² = 25
- 3³ = 27
- 25 × 27 = 675

Problem 17: 10³ - 29²
- 10³ = 1000
- 29² = 841
- 1000 - 841 = 159

Problem 18: 5³ - 3⁴
- 5³ = 125
- 3⁴ = 81
- 125 - 81 = 44

Problem 19: 10⁴ - 5⁵
- 10⁴ = 10,000
- 5⁵ = 3125
- 10,000 - 3125 = 6875

Now for the comparison problems:

Comparison 1 (already done): 5² - 3² > 30 - 4²
- Left: 25 - 9 = 16
- Right: 30 - 16 = 14
- 16 > 14 ✓

Comparison 2: 20 - 3² ___ 3² + 2³
- Left: 20 - 9 = 11
- Right: 9 + 8 = 17
- 11 < 17

Comparison 3: 4² + 6² ___ 9² - 5²
- Left: 16 + 36 = 52
- Right: 81 - 25 = 56
- 52 < 56

Comparison 4: 3³ - 2³ ___ 10² - 9²
- Left: 27 - 8 = 19
- Right: 100 - 81 = 19
- 19 = 19

Comparison 5: 2 - 5² + 3 ___ 6² - 3³ - 20
- Left: 16 - 25 + 3 = -9 + 3 = -6
- Right: 36 - 27 - 20 = 9 - 20 = -11
- -6 > -11

Final Answer:

Basic Exponents:
1) 2³ = 8
2) 4² = 16
3) 5¹ = 5
4) 10² = 100
5) 8² = 64
6) 1⁴ = 1
7) 3³ = 27
8) 10³ = 1000
9) 2⁴ = 16

Exponent Operations:
10) 3² - 2³ = 9 - 8 = 1
11) 5² + 3² = 25 + 9 = 34
12) 10² - 7² = 100 - 49 = 51
13) 3³ + 6² = 27 + 36 = 63
14) 2⁴ - 4² = 16 - 16 = 0
15) 9² - 8² = 81 - 64 = 17

Calculator Problems:
16) 5² × 3³ = 25 × 27 = 675
17) 10³ - 29² = 1000 - 841 = 159
18) 5³ - 3⁴ = 125 - 81 = 44
19) 10⁴ - 5⁵ = 10000 - 3125 = 6875

Comparisons:
20 - 3² < 3² + 2³
4² + 6² < 9² - 5²
3³ - 2³ = 10² - 9²
2⁴ - 5² + 3 > 6² - 3³ - 20