Tính giá trị biểu thức:
a. \(\dfrac{20^5\times5^{10}}{100^5}\)
b. \(\dfrac{\left(0,9\right)^5}{\left(0,3\right)^6}\)
c. \(\dfrac{6^3+3\times6^2+3^3}{-13}\)
d. \(\dfrac{4^6\times9^5+6^9\times120}{8^4\times3^{12}-6^{11}}\)
e. \(\left(2^{-1}+3^{-1}\right):\left(2^{-1}-3^{-1}\right)+\left(2^{-1}\times2^0\right)\times2^3\)
f. \(\left(\dfrac{-1}{3}\right)^{-1}-\left(\dfrac{-3}{5}\right)^6+\left(\dfrac{1}{2}\right)^2:2\)
a, \(\dfrac{20^5.5^{10}}{100^5}=\dfrac{20^5.5^{10}}{\left(20.5\right)^5}=\dfrac{20^5.5^{10}}{20^5.5^5}=5^5\)
b,\(\dfrac{\left(0,9\right)^5}{\left(0,3\right)^6}=\dfrac{\left(0,3.3\right)^5}{\left(0,3\right)^6}=\dfrac{\left(0,3\right)^5.3^5}{\left(0,3\right)^6}=\dfrac{3^5}{\left(0,3\right)}\)
c, \(\dfrac{6^3+3.6^2+3^3}{-13}=\dfrac{6^2.\left(6+3\right)+3^3}{-13}=\dfrac{6^2.9+3^3}{-13}\)=\(\dfrac{3^2.\left(36+3\right)}{-13}=\dfrac{3^2.39}{-13}=-27\)
d, \(\dfrac{4^6.9^5+6^9.120}{8^4.3^{12}-6^{11}}=\dfrac{\left(2^2\right)^6.\left(3^2\right)^5+\left(3.2\right)^9.2^3.5.3}{\left(2^3\right)^4.3^{12}-\left(2.3\right)^{11}}\)=\(\dfrac{2^{12}.3^{10}+3^9.2^9.2^3.5.3}{2^{12}.3^{12}-2^{11}.3^{11}}\)=\(\dfrac{2^{12}.3^{10}+3^{10}.2^{12}.5}{2^{11}.3^{11}.\left(2.3-1\right)}=\dfrac{2^{12}.3^{10}.\left(1+5\right)}{2^{11}.3^{11}.5}=\dfrac{2.3.6}{5}\)=\(\dfrac{36}{5}\)
e,\(\left(2^{-1}+3^{-1}\right):\left(2^{-1}-3^{-1}\right)+\left(2^{-1}.2^0\right).2^3\)
= 5 + 4
=9
