Worksheet for solving algebraic equations involving exponents, designed for educational practice.

I'll solve each algebraic equation with exponents step by step.

Let me work through all 21 problems:

Row 1:

1) x² + 101 = 110
- Subtract 101 from both sides: x² = 9
- Take square root: x = ±3

2) 2v² + 5 = 23
- Subtract 5: 2v² = 18
- Divide by 2: v² = 9
- Take square root: v = ±3

3) n³ + 6 = 33
- Subtract 6: n³ = 27
- Take cube root: n = 3

Row 2:

4) 3c² = 108
- Divide by 3: c² = 36
- Take square root: c = ±6

5) 3q² + 18 = 66
- Subtract 18: 3q² = 48
- Divide by 3: q² = 16
- Take square root: q = ±4

6) f² + 20 = 56
- Subtract 20: f² = 36
- Take square root: f = ±6

Row 3:

7) d³ + 20 = 28
- Subtract 20: d³ = 8
- Take cube root: d = 2

8) x² - 100 = 0
- Add 100: x² = 100
- Take square root: x = ±10

9) 2h² - 17 = -9
- Add 17: 2h² = 8
- Divide by 2: h² = 4
- Take square root: h = ±2

Row 4:

10) 2y² - 110 = -60
- Add 110: 2y² = 50
- Divide by 2: y² = 25
- Take square root: y = ±5

11) 3q² + 35 = 62
- Subtract 35: 3q² = 27
- Divide by 3: q² = 9
- Take square root: q = ±3

12) v² + 300 = 700
- Subtract 300: v² = 400
- Take square root: v = ±20

Row 5:

13) 2q² = 50
- Divide by 2: q² = 25
- Take square root: q = ±5

14) 3n³ + 15 = 96
- Subtract 15: 3n³ = 81
- Divide by 3: n³ = 27
- Take cube root: n = 3

15) 2e² + 30 = 230
- Subtract 30: 2e² = 200
- Divide by 2: e² = 100
- Take square root: e = ±10

Row 6:

16) 2x³ + 5 = 21
- Subtract 5: 2x³ = 16
- Divide by 2: x³ = 8
- Take cube root: x = 2

17) v² + 20 = 84
- Subtract 20: v² = 64
- Take square root: v = ±8

18) 2g² - 4 = 28
- Add 4: 2g² = 32
- Divide by 2: g² = 16
- Take square root: g = ±4

Row 7:

19) y² + 10 = 46
- Subtract 10: y² = 36
- Take square root: y = ±6

20) h² + 30 = 39
- Subtract 30: h² = 9
- Take square root: h = ±3

21) x⁴ - 6 = -2
- Add 6: x⁴ = 4
- Take fourth root: x = ±√2 (or approximately ±1.414)

Wait, let me recalculate #21 more carefully:
x⁴ - 6 = -2
x⁴ = 4
x = ±∜4 = ±√2 ≈ ±1.414

Actually, 4 can be simplified: ∜4 = (2²) = 2^(2/4) = 2^(1/2) = √2

So x = ±√2 or approximately ±1.414

Final Answer:
1) x = ±3
2) v = ±3
3) n = 3
4) c = ±6
5) q = ±4
6) f = ±6
7) d = 2
8) x = ±10
9) h = ±2
10) y = ±5
11) q = ±3
12) v = ±20
13) q = ±5
14) n = 3
15) e = ±10
16) x = 2
17) v = ±8
18) g = ±4
19) y = ±6
20) h = ±3
21) x = ±√2 (or approximately ±1.414)