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Answers
1. (4^5 × 3^7 × 2^8)/(3×64)
= (4^5 × 3^7 × 2^8)/(3×4^3)
= 4^(5-3) × 3^(7-1) × 2^8
= 4^2 × 3^6 × 2^8
= 16 × 729 × 256
= 2,985,984. (ans.)
2. 49^4 ÷ 7^9
= (7^2)^4 × 1/(7)^9
= 7^8 / 7^9
= 7^(8-9)
= 7^(-1)
= 1/7. (ans.)
3. {(9^6)^3 × 9^5} ÷ 9^24
= {9^18 × 9^5} × 1/(9^24)
= 9^(18+5) × 1/(9^24)
= 9^23 × 1/9^24
= 9^(23-24)
= 9^(-1)
= 1/9. (ans.)
4. (3^5 × 3)^3 ÷ 3^20
= (3^6)^3 × 1/(3^20)
= (3^18) × 1/(3^20)
= 3^(18-20)
= 3^(-2)
= 1/3^2
= 1/9. (ans.)
5. (50 × 5^3 × a^9) / (10^3 × a^6)
= (5 × 10 × 5^3 × a^9) / ( 10^3 × a^6)
= (5^4 × 10 × a^9) / (10^3 × a^6)
= 5^4 × 10^(-2) × a^3
= (625 a^3)/ 100 (ans.)
6. (3^6 × 10^6 × 25)/(5^8 × 6^6)
= {3^6 × (5×2)^6 × (5)^2}/{5^8 × (3×2)^6}
= (3^6 × 5^6 × 2^6 × 5^2) / (5^8 × 3^6 × 2^6)
= 5^(6+2) / 5^8
= 5^8 / 5^8
= 1 (ans.)
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