(4*3²² + 7*3²¹)*57 ÷ (19*27⁴)²
(4*3²² + 7*3²¹)*57 Factorize out 3²¹
3²¹(4*3 + 7)* 57
3²¹(12 + 7)* 57
3²¹(19)* 57. But 57 = 19 *3
3²¹(19)*(19*3)
3²¹ *3*(19)* 19.
= 3²² 19²
Bottom:
(19*27⁴)² = 19² * 27⁴ˣ²
19² * 27⁸
19² * (3³)⁸
19² * 3³ˣ⁸
=19² * 3²⁴
(3²² *19²) ÷ (19² * 3²⁴) Applying law of indices of multiplication and division
= 3²²⁻²⁴ 19²⁻²
= 3⁻² 19⁰ 19⁰ = 1
= 3⁻² * 1.
= 3⁻² = 1/3²
= 1/9
