Tính giá trị biểu thức sau bằng cách hợp lí:...

- Hướng dẫn giải

a, A = 27.36+73.99+27.14$-$49.73

= 27(36+14)+73(99$-$49)

= 27.50 + 73.50 = 50(27+73) = 50.100 = 5000

b, B = $\left(4^5.10.5^6+{25}^5.2^8\right):\left(2^8.5^4+5^7.2^5\right)$

Ta có: $4^5={\left(2^2\right)}^5=2^{2.5}=2^{10}$; ${25}^5={\left(5^2\right)}^5=5^{2.5}=5^{10}$

=> $4^5.10.5^6+{25}^5.2^8=2^{10}.2.5.5^6+5^{10}.2^8$ = $2^{11}.5^7+5^{10}.2^8$ = $2^8.2^3.5^7+5^7.5^3.2^8$ = $2^8.5^7.\left(2^3+5^3\right)$

Ta lại có: $2^8.5^4+5^7.2^5=2^5.2^3.5^4+5^4.5^3.2^5$ = $2^5.5^4.\left(2^3+5^3\right)$

Suy ra B = $2^8.5^7.\left(2^3+5^3\right)$:[$2^5.5^4.\left(2^3+5^3\right)$] = $2^8.5^7:\left(2^5.5^4\right)$

= $\left(2^8:2^5\right).\left(5^7:5^4\right)$ = $2^3.5^3={\left(2.5\right)}^3={10}^3=1000$