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Q.4 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) \(2^{10} or 10^2 \)
Answer :

(i) \( 4^3 or 3^4 \)
\(4^3 = 4 × 4 × 4 = 64, \)
\(3^4 = 3 × 3 × 3 × 3 = 81\)
Since 81 > 64
\(\therefore 3^4 > 4^3. \)
(ii)\( 5^3 or 3^5 \)
\(5^3 = 5 × 5 × 5 = 125 \)
\(3^5 = 3 × 3 × 3 × 3 × 3 = 243 \)
Since 243 > 125
\( 3^5 > 5^3. \)
(iii)\( 2^8 or 8^2 \)
\(2^8 =2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 256\)
\(8^2 = 8 × 8 = 64 \)
Since 256 > 64
\( 2^8 > 8^2.\)
(iv) \(100^2 or 2^{100}\) \(100^2 = 100 × 100 = 10000 \)
\(2^{100} = 2 × 2 × 2 × … 100 times = 214 = 16384 \)
Since 16384 > 10,000
\( 2^{100} > 100^2. \)
(v)\( 2^{10} or 10^2 \)
\(2^{10} = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 1024 \)
\(10^2 = 10 × 10 = 100 \)
\(\therefore 2^{10} >10^2. \)