Question

(75.5^4+175.5^4):(20.25.125-625.75)

[(3^2.5^2.4^3):(2^3.3^2)] .2005^0

(3.4.2^16)^2:(11.2^13.4^11-16^9)

194.12+6.437.2+3.369.4

(1^2+2^2+3^2+...+1000^2) (91-273:3)

Answer 1

a: \(=\dfrac{5^4\left(75+175\right)}{5^6\cdot4-5^4\cdot5^2\cdot3}=\dfrac{5^4\cdot250}{5^6}=10\)

b: \(=\dfrac{3^2\cdot5^2\cdot2^6}{2^3\cdot3^2}=\dfrac{5^2\cdot2^3}{1}=25\cdot8=200\)

c: \(=\dfrac{\left(3\cdot2^{18}\right)^2}{11\cdot2^{13}\cdot2^{22}-2^{36}}\)

\(=\dfrac{3^2\cdot2^{36}}{11\cdot2^{35}-2^{36}}=\dfrac{3^2\cdot2^{36}}{2^{35}\left(11-2\right)}=2\)

d: \(=12\left(194+437+369\right)=12000\)

e: \(=A\cdot\left(91-91\right)=0\)