Simplify:

(i) 

We know for any non-zero number a,

(a^m)ⁿ = a^mn

So,

As we know 4² = 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 7³ = 343

Therefore,

= 7^-2

As we know for any non-zero number a,

a^-1 = 1/a

So 7^-2= 1/7²

         = 1/49

(iii) ()^1/3 = (1 / 10³) ^1/3

= = 0.1

(iv)

We know 25 = 5²

243 = 3⁵

16 = 2⁴

8 = 2³

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 ÷ aⁿ = 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 × aⁿ = a^m+n

= 25 × 7

= 175