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}

(i) We have, 4^{3} or 3^{4}

On simplifying we get,

4^{3} = 4 × 4 × 4

= 64

And,

3^{4} = 3 × 3 × 3 × 3

= 81

Clearly,

81 > 64

Thus,

3^{4} > 4^{3}

(ii) We have, 5^{3} or 3^{5}

On simplifying we get,

5^{3} = 5 × 5 × 5

= 125

3^{5} = 3 × 3 × 3 × 3 × 3

= 243

Clearly,

243 > 125

Thus,

3^{5} > 5^{3}

(iii) We have, 2^{8} or 8^{2}

On simplifying we get,

2^{8} = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2

= 256

8^{2} = 8 × 8

= 64

Clearly,

256 > 64

Thus,

2^{8} > 8^{2}

(iv) We have, 100^{2} or 2^{100}

On simplifying we get,

100^{2} = 100 × 100

= 10000

2^{10} = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2

= 1024

Now,

2^{100} = 1024 × 1024 × 1024 × 1024 × 1024 × 1024 × 1024 × 1024 × 1024 × 1024

Clearly,

2^{100} > 10000

Thus,

2^{100} > 100^{2}

(v) W have, 2^{10} or 10^{2}

On simplifying we get,

10^{2} = 10 × 10

= 100

2^{10} = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2

= 1024

Clearly,

1024 > 100

Thus,

2^{10} > 10^{2}

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