[tex]\displaystyle\bf\\1)\\a)\\110001110=\\=0\cdot2^0+1\cdot2^1+1\cdot2^2+1\cdot2^3+0\cdot2^4+0\cdot2^5+0\cdot2^6+1\cdot2^7+1\cdot2^8=\\=1\cdot2^1+1\cdot2^2+1\cdot2^3+1\cdot2^7+1\cdot2^8=\\=2+4+8+128+256=398\\\\\boxed{\bf110001110_{(2)}=398_{(10)}}\\\\b)\\1011001=1\cdot2^0+0\cdot2^1+0\cdot2^2+1\cdot2^3+1\cdot2^4+0\cdot2^5+1\cdot2^6=\\=1\cdot2^0+1\cdot2^3+1\cdot2^4+1\cdot2^6=1+8+16+64=89\\\\\boxed{\bf1011001_{(2)}=89_{(10)}}[/tex]
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[tex]\displaystyle\bf\\c)\\1110=0\cdot2^0+1\cdot2^1+1\cdot2^2+1\cdot2^3=0+2+4+8=14\\\\\boxed{\bf1110_{(2)}=14_{(10)}}\\\\d)\\1000001001=\\=1\cdot2^0+0\cdot2^1+0\cdot2^2+1\cdot2^3+0\cdot2^4+\\+0\cdot2^5+0\cdot2^6+0\cdot2^7+0\cdot2^8+1\cdot2^9=\\=1\cdot2^0+1\cdot2^3+1\cdot2^9=1+8+512=521\\\\\boxed{\bf1000001001_{(2)}=521_{(10)}}[/tex]
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[tex]\displaystyle\bf\\2)\\a)\\363=3\times121=3\times11^2\\81=9\times9=3^4\\cmmdc=3\\cmmmc=3^4\times11^2=81\times121=9801\\\\b)\\21=3\times7\\90=2\times3^2\times5\\cmmdc=3\\cmmmc=2\times3^2\times5\times7=90\times7=630\\\\c)\\144=9\times16=2^4\times3^2\\40=8\times5=2^3\times5\\cmmdc=2^3\\cmmmc=2^4\times3^2\times5=144\times5=720[/tex]
