Question

Express each of the following as a product of prime factors only in exponential form :

(i) 216 × 384 (ii)81 × 225

please only ans no spams​

Answer 1

i. 2| 216 2| 384

2| 18 2| 192

3| 9 2| 96

3| 3 2| 48

| 1 2| 24

2| 12

2| 6

3| 3

| 1

216= 2×2×3×3 ↙️ 384=

2×2×2×2×2×2×2×3

= 2²×3² = 2⁷×3

so,

216×384= (2²×3²)×(2⁷×3)

= 2²×2⁷×3²×3

AS a^m × b^m= (a×b)^m

= 2²+⁷ × 3²+¹

= 2⁹×3³