Tính: $\frac{10^{4}.81-16.15^{2} }{4x^{4}.675}$

Đáp án: $\dfrac{10^{4}.81-16.15^{2} }{4^{4}.675}=\dfrac{14}{3}$

Giải thích các bước giải:

$\dfrac{10^{4}.81-16.15^{2} }{4^{4}.675}$

$=\dfrac{(2.5)^{4}.3^4-2^4.(3.5)^{2} }{(2^2)^{4}.(3^3.5^2)}$

$=\dfrac{2^{4}.5^{4}.3^4-2^4.3^2.5^{2} }{2^8.3^3.5^2}$

$=\dfrac{2^{4}.3^2.5^2(5^{2}.3^2-1) }{2^8.3^3.5^2}$

$=\dfrac{5^{2}.3^2-1 }{2^4.3}$

$=\dfrac{(5.3)^2-1 }{2^4.3}$

$=\dfrac{15^2-1^2 }{2^4.3}$

$=\dfrac{(15-1)(15+1) }{2^4.3}$

$=\dfrac{14.16 }{2^4.3}$

$=\dfrac{14.2^4}{2^4.3}$

$=\dfrac{14}{3}$