Tìm giá trị của biểu thức sau:
$\dfrac{2^{12}.3^{5}-4^{6}.9^{2}}{(2^{2}.3)^{6}+8^{4}.3^{5}}$ $-$ $\dfrac{5^{10}.7^{3}-25^{5}.49^{3}}{(125.7)^{3}+5^{9}.14^{3}}$
Tìm giá trị của biểu thức sau:
$\dfrac{2^{12}.3^{5}-4^{6}.9^{2}}{(2^{2}.3)^{6}+8^{4}.3^{5}}$ $-$ $\dfrac{5^{10}.7^{3}-25^{5}.49^{3}}{(125.7)^{3}+5^{9}.14^{3}}$
$\frac{2^{12}.3^{5}-4^{6}.9^{2}}{(2^{2}.3)^{6}+8^{4}.3^{5}}$ – $\frac{5^{10}.7^{3}-25^{5}.49^{3}}{(125.7)^{3}+5^{9}.14^{3}}$
=$\frac{2^{12}.3^{5}-(2^{2})^{6}.(3^{2})^{2}}{2^{12}.3^{6}+(2^{3})^{4}.3^{5}}$ – $\frac{5^{10}.7^{3}-(5^{2})^{5}.(7^{2})^{3}}{(5^{3}.7)^{3}+5^{9}.(7.2)^{3}}$
=$\frac{2^{12}.3^{5}-2^{12}.3^{4}}{2^{12}.3^{6}+2^{12}.3^{5}}$ – $\frac{5^{10}.7^{3}-5^{10}.7^{6}}{5^{9}.7^{3}+5^{9}.7^{3}.2^{3}}$
=$\frac{(2^{12}.3^{4})(3-1)}{(2^{12}.3^{4})(3^{2}+3)}$ – $\frac{(5^{9}.7^{3})(5-5.7^{3})}{(5^{9}.7^{3})(1+2^{3})}$
=$\frac{3-1}{3^{2}+3}$ – $\frac{5-5.7^{3}}{1+2^{3}}$
=$\frac{2}{12}$ – $\frac{5-5.343}{9}$
=$\frac{1}{6}$ – $\frac{-1710}{9}$
=$\frac{1}{6}$ + 190
=$\frac{1141}{6}$