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\(=\left(2^{^{2^5}}.2.5.5^6+2^8.5^{2^5}\right):\left(2^8.5^4+5^7.2^5\right)\)
=\(=\left(2^{11}.5^7+2^85^{10}\right):2^5.5^4\left(2^3+5^3\right)\)
\(=2^8.5^7\left(2^3+5^3\right):2^5.5^4\left(2^3+5^3\right)=2^8.5^7:2^5.5^4=2^3.5^3=10^3=1000\)

( 45.10.56 + 26.255 ) : ( 28.54 + 57.25 )\(=\frac{4^5.10.5^6+2^6.25^5}{2^8.5^4+5^7.2^5}\)
\(=\frac{\left(2^2\right)^5.2.5.5^6+2^6.\left(5^2\right)^5}{2^5.5^4\left(2^3+5^3\right)}\)
\(=\frac{2^{10}.2.5^7+2^6.5^{10}}{2^5.5^4\left(8+125\right)}\)
=\(\frac{2^6.5^7\left(2^4.2+5^3\right)}{2^5.5^4.133}=\frac{2.5^3\left(16.2+125\right)}{133}=\frac{2.125.157}{133}\)
\(=\frac{39250}{133}\)

A)210:28
C1: 210:28=1024:256
=4
C2: 210:28=210-8=22=4
B)46:43
C1: 46:43=4096:64=64
C2: 46:43=46-3=43=64
C)85:84
C1: 85:84=32768:4096=8
C2 85:84=85-4=81=8
D)74:74
C1: 74:74=2401:2401=1
C2 74:74=74-4=70=1
a) \(C1:2^{10}\div2^8=2^{10-8}=2^2=4\)
\(C2:2^{10}\div2^8=1024\div256=4\)
b) \(C1:4^6\div4^3=4^{6-3}=4^3=64\)
\(C2:4^6\div4^3=4096\div64=64\)
c) \(C1:8^5\div8^4=8^{5-4}=8^1=8\)
\(C2:8^5\div8^4=\left(2^3\right)^5\div\left(2^3\right)^4=2^{15}\div2^{12}=2^{15-12}=2^3=8\)
d) \(C1:7^4\div7^4=1\)
\(C2:7^4\div7^4=2401\div2401=1\)
\(B=\dfrac{4^5\cdot10\cdot5^6+25^5\cdot2^8}{2^8\cdot5^4+5^7\cdot2^5}\)
\(=\dfrac{2^{10}\cdot2\cdot5\cdot5^6+5^{10}\cdot2^8}{2^5\cdot5^4\left(2^3+5^3\right)}\)
\(=\dfrac{2^8\cdot5^7\left(2^3+5^3\right)}{2^5\cdot5^4\left(2^3+5^3\right)}=2^3\cdot5^3=10^3=1000\)
\(B=\left(4^5\cdot10\cdot5^6+25^5\cdot2^8\right):\left(2^8\cdot5^4+5^7\cdot2^5\right)\\ =\left(2^{11}\cdot5^7+5^{10}\cdot2^8\right):\left(2^8\cdot5^4+5^7\cdot2^5\right)\\ =\dfrac{2^8\cdot5^7\cdot\left(2^3+5^3\right)}{2^5\cdot5^4\cdot\left(2^3+5^3\right)}\\=2^3\cdot5^3=8\cdot125\\ =1000\)