Math practice sheet containing exercises on exponents, powers, and converting large numbers into standard form.

Let’s go through each problem one by one, solving them step by step and checking our work carefully.

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23. (–2)³¹ × (–2)¹³ = (–2)___

When multiplying powers with the same base, we add the exponents:

(–2)³¹ × (–2)¹³ = (–2)^(31 + 13) = (–2)^44

✔ Final answer for 23: 44

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24. (–3)⁸ ÷ (–3)⁵ = (–3)___

When dividing powers with the same base, subtract the exponents:

(–3)⁸ ÷ (–3)⁵ = (–3)^(8 – 5) = (–3)^3

✔ Final answer for 24: 3

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25. (11/15)⁴ × (___)⁵ = (11/15)⁹

We know that (11/15)⁴ × (11/15)⁵ = (11/15)^(4+5) = (11/15)⁹

So the blank must be (11/15)

✔ Final answer for 25: 11/15

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26. (–1/4)³ × (–1/4)^__ = (–1/4)¹¹

Add exponents: 3 + x = 11 → x = 8

✔ Final answer for 26: 8

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27. [(7/11)³]⁴ = (7/11)^__

Power of a power: multiply exponents → 3 × 4 = 12

✔ Final answer for 27: 12

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28. (6/13)¹⁰ ÷ [(6/13)⁵]² = (6/13)^__

First simplify denominator: [(6/13)⁵]² = (6/13)^(5×2) = (6/13)^10

Then: (6/13)¹⁰ ÷ (6/13)¹⁰ = (6/13)^(10–10) = (6/13)^0

✔ Final answer for 28: 0

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29. [(–1/4)¹⁶]² = (–1/4)^__

Power of a power: 16 × 2 = 32

✔ Final answer for 29: 32

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30. (13/14)⁵ ÷ (__)² = (13/14)³

Let the blank be x.

So: (13/14)⁵ ÷ x² = (13/14)³

→ x² = (13/14)⁵ ÷ (13/14)³ = (13/14)^(5–3) = (13/14)²

So x = 13/14

✔ Final answer for 30: 13/14

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31. a⁶ × a⁵ × a⁰ = a^__

Add exponents: 6 + 5 + 0 = 11

Note: a⁰ = 1, so it doesn’t change the product.

✔ Final answer for 31: 11

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32. 1 lakh = 10^__

1 lakh = 100,000 = 10⁵

✔ Final answer for 32: 5

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33. 1 million = 10^__

1 million = 1,000,000 = 10⁶

✔ Final answer for 33: 6

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34. 729 = 3^__

Try powers of 3:

3¹ = 3
3² = 9
3³ = 27
3⁴ = 81
3⁵ = 243
3⁶ = 729 ✔

✔ Final answer for 34: 6

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35. 432 = 2⁴ × 3^__

First, 2⁴ = 16

432 ÷ 16 = 27

27 = 3³

So 432 = 2⁴ × 3³

✔ Final answer for 35: 3

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36. 537000000 = __ × 10⁷

Count digits after first digit: 537000000 has 8 digits after 5? Wait — let’s write it as:

537,000,000 = 5.37 × 100,000,000 = 5.37 × 10⁸? But question says × 10⁷.

Wait — 537000000 ÷ 10⁷ = 537000000 ÷ 10000000 = 53.7

So 537000000 = 53.7 × 10⁷

But usually we use scientific notation with one digit before decimal — but the question just asks for “__ × 10⁷”, so 53.7 is correct.

Alternatively, maybe they want integer? Let’s check:

10⁷ = 10,000,000

537,000,000 ÷ 10,000,000 = 53.7

Yes, so answer is 53.7

✔ Final answer for 36: 53.7

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37. 888800000000 = __ × 10¹⁰

10¹⁰ = 10,000,000,000

888,800,000,000 ÷ 10,000,000,000 = 88.88

So 888800000000 = 88.88 × 10¹⁰

✔ Final answer for 37: 88.88

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38. 27500000 = 2.75 × 10^__

Move decimal point in 2.75 to get 27500000:

2.75 → 27.5 → 275 → 2750 → 27500 → 275000 → 2750000 → 27500000 → that’s 7 moves.

So 2.75 × 10⁷ = 27,500,000 ✔

✔ Final answer for 38: 7

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39. 340900000 = 3.409 × 10^__

Move decimal from 3.409 to 340900000:

3.409 → 34.09 → 340.9 → 3409 → 34090 → 340900 → 3409000 → 34090000 → 340900000 → 8 moves.

So 3.409 × 10⁸ = 340,900,000 ✔

✔ Final answer for 39: 8

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40. Fill in blanks with <, > or =

(a) 3² ___ 15

3² = 9 → 9 < 15 → <

(b) 2³ ___ 3²

2³ = 8, 3² = 9 → 8 < 9 → <

(c) 7⁴ ___ 5⁴

Same exponent, bigger base → 7⁴ > 5⁴ → >

(d) 10,000 ___ 10⁵

10,000 = 10⁴, 10⁵ = 100,000 → 10⁴ < 10⁵ → <

(e) 6³ ___ 4⁴

6³ = 216
4⁴ = 256
216 < 256 → <

✔ Final answers for 40:
(a) <
(b) <
(c) >
(d) <
(e) <

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Final Answer:
23. 44
24. 3
25. 11/15
26. 8
27. 12
28. 0
29. 32
30. 13/14
31. 11
32. 5
33. 6
34. 6
35. 3
36. 53.7
37. 88.88
38. 7
39. 8
40. (a) < (b) < (c) > (d) < (e)