Question

[Nguyễn Hữu Huy]

thực hiên các phép tính :

\(\frac{5.4^{15}-9^9-4.3^{20}.8^9}{5.2^9.6^{19}-7.2^{29}.27^6}\)

Answer 1

[Phước Nguyễn]

Đề như thế này chắc đúng hơn nhỉ?

\(\frac{5.14^{15}.9^9-4.3^{20}.8^9}{5.2^9.6^{19}-7.2^{29}.27^6}\)

Đặt   \(A=5.14^{15}.9^9-4.3^{20}.8^9\)  và  \(B=5.2^9.6^{19}-7.2^{29}.27^6\), ta được:

\(\text{+)}\)  \(A=5.14^{15}.9^9-4.3^{20}.8^9=5.\left(2^2\right)^{15}.\left(3^2\right)^9-2^2.3^{20}.\left(2^3\right)^9=5.2^{30}.3^{18}-2^2.3^{20}.2^{27}\)

         \(A=5.2^{30}.3^{18}-2^{29}.3^{20}=2^{29}.3^{18}\left(5.2-3^2\right)=2^{29}.3^{18}\)

\(\text{+)}\)  \(B=5.2^9.6^{19}-7.2^{29}.27^6=5.2^9.\left(2.3\right)^{19}-7.2^{29}.\left(3^3\right)^6=5.2^9.2^{19}.3^{19}-7.2^{29}.3^{18}\)

         \(B=5.2^{28}.3^{19}-7.2^{29}.3^{18}=2^{28}.3^{18}\left(5.3-7.2\right)=2^{28}.3^{18}\)

Do đó,  \(\frac{A}{B}=\frac{2^{29}.3^{18}}{2^{28}.3^{18}}=2\)

Answer 2

[Thieu Gia Ho Hoang]

bai toán này ?