[tex]\displaystyle\bf\\10\times\left\{24^2:576+3\times\left[\Big(3^2\times2\Big)^{15}:\Big(3^{29}\times2^{15}\Big)+1^{21}\right]\right\}:13=\\\\\\=10\times\left\{576:576+3\times\left[\Big(3^{2\times15}\times2^{15}\Big):\Big(3^{29}\times2^{15}\Big)+1^{21}\right]\right\}:13=\\\\\\=10\times\left\{576:576+3\times\left[\Big(3^{30}\times2^{15}\Big):\Big(3^{29}\times2^{15}\Big)+1^{21}\right]\right\}:13=[/tex]
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[tex]\displaystyle\bf\\=10\times\left\{1+3\times\left[\Big(3^{30-29}\times2^{15-15}\Big)+1\right]\right\}:13=\\\\\\=10\times\left\{1+3\times\left[\Big(3^{1}\times2^{0}\Big)+1\right]\right\}:13=\\\\\\=10\times\left\{1+3\times\Big[3\times1+1\Big]\right\}:13=\\\\\\=10\times\Big\{1+3\times4\Big\}:13=\\\\\\=10\times\Big\{1+12\Big\}:13=\\\\\\=10\times13:13=130:13=\boxed{\bf10}[/tex]
