Answer :

**(i)**

We know for any non-zero number a,

(a^{m})^{n} = a^{mn}

So,

As we know 4^{2} = 16

Therefore,

= 4^{-1}

As we know for any non-zero number a,

a^{-1} = 1/a

So 4^{-1} = 1/4

**(ii)** [(343)^{-2}]^{1/3}

We know for any non-zero number a,

(a^{m})^{n} = a^{mn}

So,

As we know 7^{3} = 343

Therefore,

= 7^{-2}

As we know for any non-zero number a,

a^{-1} = 1/a

So 7^{-2}= 1/7^{2}

= 1/49

(iii) ()^{1/3} = (1 / 10^{3}) ^{1/3}

= = 0.1

(iv)

We know 25 = 5^{2}

243 = 3^{5}

16 = 2^{4}

8 = 2^{3}

So,

We know for any non-zero number a,

(a^{m})^{n} = a^{mn}

So,

(v)

We know that for any non-zero number a,

a^{m} ÷ a^{n} = a^{m-n}

So,

As we know for any non-zero number a,

a^{-1} = 1/a

(vi)

We know for any non-zero number a,

(a^{m})^{n} = a^{mn}

So,

We know for any non-zero number a,

a^{m} × a^{n} = a^{m+n}

= 25 × 7

= 175

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