Question

[GT 6916]

Viết các biểu thức sau dưới dạng lũy thừa của một số hữu tỉ :

1)\(\frac{8^{11}.3^{17}}{27^{10}.9^{15}}\)

2)\(\frac{\left(5^4-5^3\right)^3}{125^4}\)

3)\(\frac{4^{20}-2^{20}+6^{20}}{6^{20}-3^{20}+9^{20}}\)

Answer 1

[Yen Nhi]

\(\frac{8^{11}.3^{17}}{27^{10}.9^{15}}=\frac{8^{11}.3^{17}}{3^{30}.3^{30}}=\frac{8^{11}}{3^{13}.3^{30}}=\frac{8^{11}}{3^{43}}\)

\(\frac{\left(5^4-5^3\right)^3}{125^4}=\frac{[\left(5-1\right).5^3]^3}{5^{12}}=\frac{\left(4.5^3\right)^3}{5^{12}}=\frac{64.5^9}{5^{12}}=\frac{64}{5^3}=\left(\frac{4}{5}\right)^3\)

\(\frac{4^{20}-2^{20}+6^{20}}{6^{20}-3^{20}+9^{20}}=\frac{2^{40}-2^{20}+6^{20}}{6^{20}-3^{20}+3^{40}}=\frac{2^{20}.\left(2^{20}-1+3^{30}\right)}{3^{20}.\left(2^{20}-2+3^{20}\right)}=\frac{2^{20}}{3^{20}}=\left(\frac{2}{3}\right)^{20}\)