Question

ordonati crescator: 8×9^6+(9^2)^3 ; (5^3)^4 ×25 ; 4^17:2^13

Answer 1

$\it a=8\cdot9^6+(9^2)^3 =8\cdot9^6+9^6 =9^6(8+1)=9^6\cdot9=9^7\\ \\ b=(5^3)^4\cdot25=5^{12}\cdot25= (5^2)^6\cdot25=25^6\cdot25=25^7\\ \\ c=4^{17}:2^{13}=(2^2)^{17}:2^{13} =2^{34}:2^{13} =2^{21} = (2^3)^7=8^7\\ \\ 8^7 < 9^7 <25^7 \Longrightarrow c<a<b$

Answer 2

8ₓ9⁶ + 9²⁾³ = 8ₓ9⁶ + 9⁶ = 9⁶(8 + 1) = 9⁷

5³⁾⁴ₓ25 = 5¹²ₓ25 = 5²⁾⁶ₓ25 = 25⁶ₓ25 = 25⁷

4¹⁷ : 2¹³ = 2²⁾¹⁷ : 2¹³ = 3³⁴ : 2¹³ = 2²¹ = 2³⁾⁷ = 8⁷

8⁷ < 9⁷ < 25⁷