Answer:
4.
a. 1000
b. 21^16
c. 10^40
d. 35^10 × 1225^3
5.
a. 64
b. 256
c. 2^30
d. 3^12
Explanation:
4.
a. 2³ × 5³ = (2 × 5)³ = 10³ = 1000
b. (3^9 × 7^9) × (3^7 × 7^7) = (3 × 7)^9 × (3 × 7)^7 = 21^9 × 21^7 = 21^16
c. (2^20 × 5^20) × (4^10 × 25^10) = (2 × 5)^20 × (4 × 25)^10 = 10^20 × 100^10 = 10^20 × (10^2)^10 = 10^20 × 10^20 = 10^40
d. (7^10 × 5^10) × (49^3 × 25^3) = 35^10 × 1225^3
5.
a. 12^6 : 6^6 = (12:6)^6 = 2^6 = 64
b. 30^8 : 15^8 = (30 : 15)^8 = 2^8 = 256
c. (20^30 : 5^30) : (4^30 : 2^30) = 4^30 : 2^30 = 2^30
d. (30^12 : 5^12) : (6^12 : 3^12) = 6^12 : 2^12 = 3^12