Identify the greater number, wherever possible, in each of the following?
(i) 4³ or 3⁴ (ii) 5³ or 3⁵ (iii) 2⁸ or 8² (iv) 100² or 2¹⁰⁰ (v) 2¹⁰ or 10²

Solution:

Here, we know the base and exponent.

We will solve by expanding the number and then compare the two numbers to find which is greater.

(i) 4³ or 3⁴

4 × 4 × 4 = 64

3 × 3 × 3 × 3 = 81

Since 81 > 64

So, 3⁴ is greater than 4³

(ii) 5³ or 3⁵

5 × 5 × 5 =125

3 × 3 × 3 × 3 × 3 = 243

Since 243 > 125

So, 3⁵ is greater than 5³

(iii) 2⁸ or 8²

2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 256

8 × 8 = 64

Since 256 > 64

So, 2⁸ is greater than 8²

(iv) 100² or 2¹⁰⁰

100 × 100 = 10,000

Let's first calculate the value of  2¹⁰

2¹⁰ = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 1024

Now, (1024)¹⁰ = 1024 × 1024 × 1024 × 1024 × 1024 × 1024 × 1024 × 1024 × 1024 × 1024

Clearly (1024)¹⁰ > 10,000

So, 2¹⁰⁰ is greater than 100²

(v) 2¹⁰ or 10²

2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 1024

10 ×  10 = 100

Since 1024 > 100

So, 2¹⁰ is greater than 10²

☛ Check: NCERT Solutions Class 7 Maths Chapter 13

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Video Solution:

Identify the greater number, wherever possible, in each of the following? (i) 4³ or 3⁴ (ii) 5³ or 3⁵ (iii) 2⁸ or 8² (iv) 100² or 2¹⁰⁰ (v) 2¹⁰ or 10²

Maths NCERT Solutions Class 7 Chapter 13 Exercise 13.1 Question 4

Summary:

The greater number, in each of the following (i) 4³ or 3⁴ (ii) 5³ or 3⁵ (iii) 2⁸ or 8² (iv) 100² or 2¹⁰⁰ (v) 2¹⁰ or 10² is (i) 3⁴ is greater than 4³ since 81 > 64; (ii) 3⁵ is greater than 5³ since 243 > 125; (iii) 2⁸ is greater than 8² since 256 > 64, (iv) 2¹⁰⁰ is greater than 100² since (1024)¹⁰ > 10,000 (v) 2¹⁰ is greater than 10² since 1024 > 100.

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