Question

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

1. \(4 ^3\) or \(3^4\) 
2.  \(5 ^3\) or \(3^5\) 
3.  \(2 ^8\) or \(8^2\) 
4.  \(100^2\) or \(2^{100}\) 
5.  \(2 ^{10}\) or \(10^{2}\)

Answer 1

(i) \(4^3 = 4 \times 4 \times 4 = 64\) 
\(3^ 4 = 3 \times 3 \times 3 \times 3 = 81\) 
Therefore, \(34 > 43\)

---

(ii) \(5^3 = 5 \times 5 \times 5 =125\) 
\(3^ 5 = 3 \times 3 \times 3 \times 3 \times 3 = 243\) 
Therefore, \(35 > 53\)

---

(iii) \(2^8 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 = 256\) 
\(8^ 2 = 8 \times 8 = 64\) 
Therefore, \(28 > 82\)

---

 (iv) \(100^2\) or \(2^{100}\) 
\(2^{ 10 }= 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 = 1024\) 
\(2^{ 100}\) = \(1024 \times 1024 \times 1024 \times 1024 \times 1024 \times 1024 \times 1024 \times 1024 \times 1024 \times 1024\) 
\(100^2 = 100 \times 100 = 10000\) 
Therefore, \(2^{100} > 100^2\)

---

 (v) \(2^{10}\) and \(10^2\) 
\(2^{ 10 }= 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 = 1024\) 
\(10^2 = 10 \times 10 = 100\) 
Therefore, \(2^{10} > 10^2\)