Question

Viết các kết quả sau dưới dạng một lũy thừa :

a) 125^{5 :} 25³

b) 27⁶ : 9³

c) 4²⁰ : 2¹⁵

d) 24ⁿ : 2²ⁿ

e) 64⁴ x 16⁵ :4²⁰

g) 32⁴ : 8⁶

Answer 1

a125^5:25^3=(5^3)^5:(5^2)^3=5^15:5^6=5^9

b27^6:9^3=(3^3)^6:(3^2)^3=3^18:3^6=3^13

c  4^20:2^15=(2^2)^20:2^15=2^40:2^15=2^25

d24^n:2^2.n=24^n:(2^2)^n=24^n:4^n=(24:4)^n=6^n

e 64^4 . 16^5:4^20=(2^6)^4 . (2^4)^5 :(2^2)^20=2^24 . 2^20:2^40=2^4

g 32^4:8^6=(2^5)^4:(2^3)^6=2^20:2^18=2^2

Answer 2

a, \(125^5:25^3=\left(5^3\right)^5:\left(5^2\right)^3=5^{15}:5^6=5^9\)

b, \(27^6:9^3=\left(3^3\right)^6:\left(3^2\right)^3=3^{18}:3^6=3^{12}\)

c, \(4^{20}:2^{15}=\left(2^2\right)^{20}:2^{15}=2^{40}:2^{15}=2^{25}\)

d, \(24^n:2^{2.n}=2^n.12^n:2^n.2^n=12^n:2^n=2^n.6^n:2^n=6^n\)

e, \(64^4.16^5:4^{20}=4^{12}.4^{10}:4^{20}=4^{12+10-20}=4^2\)

g, \(32^4:8^6=8^4.4^4:8^4.8^2=4^4:4^2.2^2=4^2.2^2=2^4.2^2=2^6\)