Question

[Học]

So Sánh

a, \(\left(\frac{1}{8}\right)^7;\left(\frac{1}{243}\right)^6\)

b,\(\left(\frac{3}{8}\right)^5;\left(\frac{5}{243}\right)^3\)

Answer 1

[Ngọc Lan Tiên Tử]

\(a,\left(\frac{1}{8}\right)^7>\left(\frac{1}{81}\right)^7=\left(\frac{1}{3^4}\right)^7=\frac{1}{3^{28}}\)

\(\left(\frac{1}{234}\right)^6=\left(\frac{1}{3^5}\right)^6=\frac{1}{3^{30}}\)

Vì \(\frac{1}{3^{28}}>\frac{1}{3^{30}}\)nên \(\left(\frac{1}{80}\right)^7>\left(\frac{1}{243}\right)^8\)

\(b,\left(\frac{3}{5}\right)^5=\left(\frac{3}{2^3}\right)^5=\frac{243}{2^{15}};\)

\(\left(\frac{5}{243}\right)^3=\left(\frac{5}{3^5}\right)^3=\frac{125}{3^{15}}\)

Chọn phân số \(\frac{243}{3^{15}}\)làm phân số trung gian để so sánh hai phân số trên , ta thấy :

\(\frac{243}{2^{15}}>\frac{243}{3^{15}}>\frac{125}{3^{15}}\)

=> \(\frac{243}{2^{15}}>\frac{125}{3^{15}}\)

Từ đó => \(\left(\frac{3}{8}\right)^5>\left(\frac{5}{243}\right)^3\)