Question

Rút gọn các biểu thức

b) \(\frac{36^7}{2^{15}.27^5}\)

c) \(\frac{2^7.3^6}{6^5.8^2}\)

e) \(\frac{81^5.125^{10}}{75^{15}}\)

Thanks <3

Answer 1

b)\(\frac{1}{6}\)

c)\(\frac{3}{16}\)

e)243

Answer 2

a)\(\frac{36^7}{2^{15}\cdot27^5}=\frac{36^7}{\left(2^3\right)^5\cdot27^5}\)

\(=\frac{36^7}{\left(8\cdot27\right)^5}=\frac{36^7}{216^5}\)

\(=\frac{36^7}{36^5\cdot6^5}=\frac{36^5\cdot36^2}{36^5\cdot6^5}\)

\(=\frac{36^2}{6^5}=\frac{\left(6^2\right)^2}{6^5}=\frac{6^4}{6^5}=\frac{1}{6}\)

\(\)

Answer 3

\(\frac{2^7\cdot3^6}{6^5\cdot8^2}=\frac{2^7\cdot3^6}{6^5\cdot\left(2^3\right)^2}=\frac{2\cdot3^6}{6^5}\)

\(=\frac{2\cdot3^6}{\left(3\cdot2\right)^5}=\frac{2\cdot3^6}{3^5\cdot2^5}\)

\(=\frac{3}{2^4}=\frac{3}{16}\)