Say true or false and justify your answer:

(i) 10 × 10^{11} = 100^{11}

(ii) 2^{3} > 5^{2}

(iii) 2^{3} × 3^{2} = 6^{5}

(iv) 3^{0} = (1000)^{0}

(i) We have,

10 × 10^{11} = 100^{11}

L.H.S. = 10 × 10^{11}

Using identity: (a^{m} × a^{n} = a^{m + n})

= 10^{11 + 1}

= 10^{12}

R.H.S. = 100^{11}

= (10 × 10)^{11}

= (10^{2})^{11}

Using identity: (a^{m})^{n} = a^{mn}

= 10^{2 × 11}

= 10^{22}

So, it is clear that

L.H.S. R.H.S.

∴ The statement given in the question is false

(ii) We have,

2^{3} > 5^{2}

L.H.S. = 2^{3}

= 2 × 2 × 2

= 8

R.H.S. = 5^{2}

= 5 × 5

= 25

Since,

It is clear that 25 > 8

∴ The statement given in the question is false

(iii) We have,

2^{3} × 3^{2} = 6^{5}

L.H.S. = 2^{3} × 3^{2}

= 2 × 2 × 2 × 3 × 3

= 72

R.H.S. = 6^{5}

= 6 × 6 × 6 × 6 × 6

= 7776

It is clear that

L.H.S. R.H.S.

∴ The statement given in the question is false

(iv) We have,

3^{0} = (1000)^{0}

L.H.S. = 3^{0}

= 1

R.H.S. = (1000)^{0}

= 1

Hence,

L.H.S. = R.H.S.

∴ The statement given in the question is true

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