# Identify the greater number, wherever possible, in each of the following?

(i) 4^{3} or 3^{4 }(ii) 5^{3 }or 3^{5 }(iii) 2^{8 }or 8^{2 }(iv) 100^{2 }or 2^{100} (v) 2^{10} or 10^{2}

**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) 4^{3} or 3^{4}

4 × 4 × 4 = 64

3 × 3 × 3 × 3 = 81

Since 81 > 64

So, 3^{4} is greater than 4^{3}

(ii) 5^{3} or 3^{5}

5 × 5 × 5 =125

3 × 3 × 3 × 3 × 3 = 243

Since 243 > 125

So, 3^{5} is greater than 5^{3}

(iii) 2^{8} or 8^{2}

2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 256

8 × 8 = 64

Since 256 > 64

So, 2^{8} is greater than 8^{2}

(iv) 100^{2} or 2^{100}

100 × 100 = 10,000

Let's first calculate the value of 2^{10}

2^{10} = 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, 2^{100} is greater than 100^{2}

(v) 2^{10} or 10^{2}

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

10 × 10 = 100

Since 1024 > 100

So, 2^{10} is greater than 10^{2}

**☛ Check: **NCERT Solutions Class 7 Maths Chapter 13

**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) 4^{3} or 3^{4 }(ii) 5^{3 }or 3^{5 }(iii) 2^{8 }or 8^{2 }(iv) 100^{2 }or 2^{100} (v) 2^{10} or 10^{2} is (i) 3^{4} is greater than 4^{3} since 81 > 64; (ii) 3^{5} is greater than 5^{3} since 243 > 125; (iii) 2^{8} is greater than 8^{2} since 256 > 64, (iv) 2^{100} is greater than 100^{2} since (1024)^{10} > 10,000 (v) 2^{10 }is greater than 10^{2} since 1024 > 100.

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