Simplify:

(i)

(ii)

(iii)

We have,

Using identity: (a^m)ⁿ = a^mn , we get,

Using identity: (a^m)ⁿ = a^mn, we get,

=

Using identity: (a^m aⁿ = a^{m - n})

= 2^{10 - 9} × 7^{3 – 1}

= 2¹ × 7²

= 2 × 7 × 7

= 98

(ii) We have,

Using identity: [(a × b)^m = a^m ×b^m]

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

=

By using (a^m aⁿ = a^{m - n}), we get:

=

=

(iii) We have,

=

Using identity: [(a × b)^m = a^m ×b^m]

=

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

By using (a^m aⁿ = a^{m - n}), we get:

= 3^{5 – 5} × 2^{5 – 5} × 5^{7 – 7}

= 3⁰ × 2⁰ × 5⁰

= 1 × 1 × 1

= 1