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a)\(\left(10^2+11^2+12^2\right)\div\left(13^2+14^2\right)\)
\(=\left(100+121+144\right)\div\left(169+196\right)\)
\(=365\div365\)
\(=1\)
b) \(1.2.3...9-1.2.3...8-1.2.3...8^2\)
\(=1.2.3...8\left(9-1-8\right)\)
\(=1.2.3...8.0\)
\(=0\)
d) \(1152-\left(374+1152\right)+\left(-65+374\right)\)
\(=1152-374-1152-65+374\)
\(=\left(1152-1152\right)-65+\left(374-374\right)\)
\(=0-65+0\)
\(=-65\)
e) \(13-12+11+10-9+8-7-6+5-4+3+2-1\)
\(=13-\left(12-11\right)+\left(10-9\right)+\left(8-7\right)-\left(6-5\right)-\left(4-3\right)\)\(+\left(2-1\right)\)
\(=13-1+1+1-1-1+1\)
\(=13+0+0+0\)
\(=13\)
a) \(\frac{16.64.8^2}{4^3.2^5.16}=\frac{16.4^3.\left(2^3\right)^2}{4^3.2^5.16}=\frac{16.4^3.2^6}{4^3.2^5.16}=2\)
\(\frac{64^2.81^3.34}{2^{13}.3^9.17}=\frac{\left(2^6\right)^2.\left(3^4\right)^3.2.17}{2^{13}.3^9.17}=\frac{2^{13}.3^{12}.17}{2^{13}.3^9.17}=3^3=27\)
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