a) \(\frac{20^5.5^{10}}{100^5}=\frac{20^5.5^5.5^5}{100^5}=\frac{\left(20.5.5\right)^5}{100^5}\)
\(=\frac{500^5}{100^5}=\left(\frac{500}{100}\right)^5=5^5=3125\)
b) \(\frac{\left(0,9\right)^5}{\left(0,3\right)^6}=\frac{\left(0,9\right)^5.1}{\left(0,3\right)^5.0,3}=\left(\frac{0,9}{0,3}\right)^5.\frac{1}{0,3}\)
\(=3^5.\frac{1}{0,3}=3^4.3.\frac{1}{0,3}=81.10=810\)
c) \(\frac{6^3+3.6^2+3^3}{-13}=\frac{2^3.3^3+3.2^2.3^2+3^3}{-13}\)
\(=\frac{2^3.3^3+3^3.2^2+3^3}{-13}=\frac{3^3.\left(2^3+2^2+1\right)}{-13}\)
\(=\frac{3^3.13}{-13}=-3^3=-27\)
d) \(4^6.9^5+6^9.120=\left(2^2\right)^6.\left(3^2\right)^5+\left(2.3\right)^9.2^3.3.5\)
\(=2^{12}.3^{10}+2^9.3^9.2^3.3.5\)
\(=2^{12}.3^{10}+2^{12}.3^{10}.5\)
\(=2^{12}.3^{10}.\left(1+5\right)\)
\(=2^{12}.3^{10}.6\)
\(=2^{12}.3^{10}.2.3\)
\(=2^{13}.3^{11}\)
\(=1451188224\)
84.312 - 611
= (23)4.312 - 211.311
= 212.312 - 211.311
= 211.311.(2.3 - 1)
= 211.311.5
213.311 : (211.311.5)
= 4 : 5
= 0,8
