\(2010-2000:\left[486-2.\left(7^2-6\right)\right]\)
\(=2010-2000:\left[486-2.\left(49-6\right)\right]\)
\(=2010-2000:\left[486-2.43\right]\)
\(=2010-2000:\left[486-86\right]\)
\(=2010-2000:400\)
\(=2010-5\)
\(=2005\)
\(500-\left\{5.\left[409-\left(2^3:3-21\right)^2\right]+10^3\right\}.15\)
\(=500-\left\{5.\left[409-\left(8:3-21\right)^2\right]+10^3\right\}.15\)
\(=500-\left\{5.\left[409-\left(\frac{8}{3}-21\right)^2\right]+10^3\right\}.15\)
\(=500-\left\{5.\left[409-\frac{-55}{3}\right]+1000\right\}.15\)
\(=500-\left\{5.\left(\frac{1282}{3}\right)+1000\right\}.15\)
\(=500-\left\{\frac{6410}{3}+1000\right\}.15\)
\(=500-\frac{9410}{3}.15\)
\(=500-47050\)
\(=-46550\)
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