Laws of Exponents - Taking Power of a Power

If a is a non-zero rational number and m and n are integers, then (a^m)ⁿ = a^{m × n} = a^mn.

Taking Power of a Power:

If a is a non-zero rational number and m and n are integers, then (a^m)ⁿ = a^{m × n} = a^mn.

(i) (3²)⁴

= 3² × 3² × 3² × 3²

= 3^{2 + 2 + 2 + 2}

= 3⁸.....(Observe 8 is the product of 2 and 4).

= 3^{2 × 4}..............[ (a^m)ⁿ = a^{m × n} ]

(ii) (7²)¹⁰

= 7^{2 × 10}

= 7²⁰..............[ (a^m)ⁿ = a^{m × n} ]

(iii) (3⁴)³ 

= 3^{4 × 3} 

= 3¹² ................[ (a^m)ⁿ = a^{m × n} ]