Let’s solve each of the 24 problems one by one, using basic arithmetic and index (exponent) laws. After solving each, we’ll note the answer and cross it off from the list 1–24.
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Problem 1:
7⁵ × □² = 7⁷
→ Use index law: *a^m × a^n = a^(m+n)*
So, 7⁵ × 7² = 7⁷ → So □² must be 7² → □ =
7
✔ Answer:
7
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Problem 2:
3⁴ = □²
→ 3⁴ = (3²)² = 9² → So □ =
9
✔ Answer:
9
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Problem 3:
2² × 3 = □
→ 4 × 3 =
12
✔ Answer:
12
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Problem 4:
2³ × 2⁵ = 2^□
→ 2^(3+5) = 2⁸ → □ =
8
✔ Answer:
8
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Problem 5:
2³ × 3 = □
→ 8 × 3 =
24
✔ Answer:
24
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Problem 6:
□² = 100
→ √100 =
10
✔ Answer:
10
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Problem 7:
2¹ × 11¹ = □
→ 2 × 11 =
22
✔ Answer:
22
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Problem 8:
2² × 5 = □
→ 4 × 5 =
20
✔ Answer:
20
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Problem 9:
6² − 5² = □
→ 36 − 25 =
11
✔ Answer:
11
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Problem 10:
23¹ = □
→ Any number to power 1 is itself →
23
✔ Answer:
23
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Problem 11:
□² = 361
→ √361 =
19 (since 19×19=361)
✔ Answer:
19
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Problem 12:
3⁷ × 3⁷ × 3⁷ = 3^□
→ Add exponents: 7 + 7 + 7 =
21
✔ Answer:
21
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Problem 13:
3 × 3 × 3 × 3 = 3^□
→ That’s 3⁴ → □ =
4
✔ Answer:
4
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Problem 14:
2¹ × 3¹ = □
→ 2 × 3 =
6
✔ Answer:
6
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Problem 15:
□³ = 8
→ Cube root of 8 =
2
✔ Answer:
2
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Problem 16:
□² = 9
→ √9 =
3
✔ Answer:
3
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Problem 17:
2⁴ + 1 = □
→ 16 + 1 =
17
✔ Answer:
17
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Problem 18:
6⁰ = □
→ Any non-zero number to power 0 is
1
✔ Answer:
1
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Problem 19:
2 × 3² = □
→ 2 × 9 =
18
✔ Answer:
18
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Problem 20:
2³ × 2⁵ × 2⁷ = 2^□
→ Add exponents: 3 + 5 + 7 =
15
✔ Answer:
15
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Problem 21:
2² + 3² = □
→ 4 + 9 =
13
✔ Answer:
13
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Problem 22:
□² × 2² = 100
→ □² × 4 = 100 → □² = 25 → □ =
5
✔ Answer:
5
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Problem 23:
2⁴ = □
→ 16
✔ Answer:
16
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Problem 24:
14 = □¹
→ Any number to power 1 is itself → □ =
14
✔ Answer:
14
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✔ Final Answers (in order 1 to 24):
1.
7
2.
9
3.
12
4.
8
5.
24
6.
10
7.
22
8.
20
9.
11
10.
23
11.
19
12.
21
13.
4
14.
6
15.
2
16.
3
17.
17
18.
1
19.
18
20.
15
21.
13
22.
5
23.
16
24.
14
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📌 All numbers from 1 to 24 are used exactly once — perfect!
You can now cross them off the list as you go.
Let me know if you’d like this formatted into a grid or printable version!
Parent Tip: Review the logic above to help your child master the concept of math worksheet for grade 9.
