a) 5^16 . 27^7; b) (-0,2)^2 . 5 - (2^3 . 27^3) / (4^6 . 9^5);

* Hướng dẫn giải

a) $\frac{5^{16}{.27}^7}{{125}^5{.9}^{11}}=\frac{5^{16}.{\left(3^3\right)}^7}{{\left(5^3\right)}^5.{\left(3^2\right)}^{11}}$

$=\frac{5^{16}{.3}^{3.7}}{5^{3.5}{.3}^{2.11}}=\frac{5^{16}{.3}^{21}}{5^{15}{.3}^{22}}=\frac{5}{3}$

b) ${\left(-0,2\right)}^2.5-\frac{2^3{.27}^3}{4^6{.9}^5}$

$={\left(\frac{-1}{5}\right)}^2.5-\frac{2^3.{\left(3^3\right)}^3}{{\left(2^2\right)}^6.{\left(3^2\right)}^5}$

$=\frac{1}{25}.5-\frac{2^3{.3}^9}{2^{12}{.3}^{10}}$

$=\frac{1}{5}-\frac{1}{2^9.3}$

$=\frac{1}{5}-\frac{1}{1536}$

$=\frac{1536}{7680}-\frac{5}{7680}$

$=\frac{1531}{7680}$

c) $\frac{5^6+2^2{.25}^3+2^3{.125}^2}{{26.5}^6}$

$=\frac{5^6+2^2.{\left(5^2\right)}^3+2^3.{\left(5^3\right)}^2}{{26.5}^6}$

$=\frac{5^6+2^2{.5}^6+2^3{.5}^6}{{26.5}^6}$

$=\frac{5^6.\left(1+2^2+2^3\right)}{{26.5}^6}$

$=\frac{5^6.13}{{26.5}^6}=\frac{13}{26}=\frac{1}{2}$