(i) We know that, (a^m × aⁿ = a^{m + n})

Thus,

3² × 3⁴ × 3⁸

= (3)^{2 + 4 + 8}

= 3¹⁴

(ii) We have,

6¹⁵ 6¹⁰

We know that,

(a^m aⁿ = a^{m - n})

Thus,

6¹⁵ 6¹⁰

= (6)^{15 - 10}

= 6⁵

(iii) We have,

a³ × a²

We know that,

(a^m × aⁿ = a^{m + n})

Therefore,

a³ × a²

= (a)^{3 + 2}

= a⁵

(iv) We have,

7^x × 7²

We know that,

(a^m × aⁿ = a^{m + n})

Thus,

7^x × 7²

= (7)^{x + 2}

(v) We have,

(5²)³ 5³

Using identity:

(a^m)ⁿ = a^{m × n}

= 5^{2 × 3} 5³

= 5⁶ 5³

We know that,

(a^m aⁿ = a^{m - n})

Thus,

5⁶ 5³

= (5)^{6 - 3}

= 5³

(vi) We have,

2⁵ × 5⁵

We know that,

[a^m × b^m = (a × b)^m]

Thus,

2⁵ × 5⁵

= (2 × 5)^{5 + 5}

= 10⁵

(vii) We have,

a⁴ × b⁴

We know that,

[a^m × b^m = (a × b)^m]

Thus,

a⁴ × b⁴

= (a × b)⁴

(viii) We have,

(3⁴)³

We know that,

(a^m)ⁿ = a^mn)

Thus,

(3⁴)³

= (3⁴)³

= 3¹²

(ix) We have,

(2²⁰ 2¹⁵) × 2³

We know that,

(a^m aⁿ = a^{m - n})

Thus,

(2^{20 - 15}) × 2³

= (2)⁵ × 2³

We know that,

(a^m × aⁿ = a^{m + n})

Thus,

(2)⁵ × 2³

= (2^{5 + 3})

= 2⁸

(x) We have,

(8^t 8²)

We know that,

(a^m aⁿ = a^{m - n})

Thus,

(8^t 8²)

= (8^{t – 2})