Example 12 (i) - Chapter 11 Class 7 Exponents and Powers
Last updated at Dec. 16, 2024 by Teachoo
Last updated at Dec. 16, 2024 by Teachoo
Example 12 Simplify and write the answer in the exponential form (i) (〖12〗^4 × 〖 9〗^3 × 4)/(6^3 ×〖 8〗^2 × 27) (〖12〗^4 × 9^3 × 4)/(6^3 × 8^2 × 27) = ((2 × 2 × 3)^4 × (3 × 3)^3 × (2 × 2))/((2 × 3)^3 × 〖(2 × 2 × 2)〗^2 × (3 × 3 × 3)) = ((2^2 × 3)^4 × (3^2 )^3 × (2^2 ))/((2 × 3)^3 × 〖(2^3)〗^2 × (3^3)) = ((2^2 )^4 × (3)^4 × (3^2 )^3 × (2^2))/(2^3 × 3^3 × (2^3 )^2×〖 3〗^3 ) = (2^(2 × 4) × 3^4 × 3^(2 × 3) ×〖 2〗^2)/(2^3 × 3^3 × 2^(3 × 2) × 3^3 ) [(a × b)m = am × bm] [(am)n = am × n] = (2^8 × 3^4 × 3^6 ×〖 2〗^2)/(2^3 × 3^3 × 2^6 × 3^3 ) = ((2^8 ×〖 2〗^2 ) × (3^4 × 3^6))/((2^3 × 2^6 ) × (3^3 × 3^3)) = (2^(8 + 2) × 3^(4 + 6))/(2^(3 + 6) ×〖 3〗^(3 + 3) ) = 2^10/2^9 × 3^10/3^6 = 210 − 9 × 310 − 6 = 21 × 34 = 2 × 81 = 162 (Using am × an = am + n) (Using 𝑎^𝑚/𝑎^𝑛 = am − n)
Examples
Example 2 Important
Example 3
Example 4 Important
Example 5 (i)
Example 5 (ii) Important
Example 5 (iii)
Example 5 (iv) Important
Example 6
Example 7 Important
Example 8 (i) Important
Example 8 (ii)
Example 8 (iii) Important
Example 9 (i)
Example 9 (ii) Important
Example 10 Important
Example 11 (i)
Example 11 (ii)
Example 11 (iii)
Example 11 (iv) Important
Example 11 (v) Important
Example 12 (i) You are here
Example 12 (ii) Important
Example 12 (iii) Important
Example 13 (i)
Example 13 (ii) Important
Example 13 (iii)
Example 13 (iv) Important
About the Author
Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo