Question

Tính

a)\(\dfrac{6^6+6^3.3^3+3^6}{-73}\)

b)\(\dfrac{8^{20}+4^{20}}{4^{25}+64^5}\)

c)\(\dfrac{45^{10}.5^{20}}{75^{15}}\)

Answer 1

a)\(\dfrac{6^6+6^3.3^3+3^6}{-73}\)\(=\dfrac{2^6.3^6+2^3.3^3.3^3+3^6}{-73}=\dfrac{2^6.3^6+2^3.3^6+3^6.1}{-73}\)

\(=\dfrac{3^6.\left(2^6+2^3+1\right)}{-73}=\dfrac{3^6\left(64+8+1\right)}{-73}=^{ }\)\(\dfrac{3^6.73}{-73}=\dfrac{3^6}{-1}=-3^6\)

b)\(\dfrac{8^{20}+4^{20}}{4^{25}+64^5}=\dfrac{2^{60}+2^{40}}{2^{50}+2^{30}}=\dfrac{2^{40}.\left(2^{20}+1\right)}{2^{30}.\left(2^{20}+1\right)}=\dfrac{2^{40}}{2^{30}}=2^{10}=1024\)

c)\(\dfrac{45^{10}.5^{20}}{75^{15}}=\dfrac{\left(3^2\right)^{10}.5^{10}.5^{20}}{\left(5^2\right)^{15}.3^{15}}=\dfrac{3^{20}.5^{30}}{5^{30}.3^{15}}=3^5=243\)