\( 66 \{ 5 \times [ 2 \times 5 - 2 \times ( 21 - 5 \times 2 ^ { 2 } ) ^ { 2 } ] ^ { 2 } \} : ( 2 ^ { 3 } \times 10 ) + [ 19 : ( 3 + 2 \times 8 ) ] ^ { 2 } , \{ ( 2 ^ { 2 } \times 3 ^ { 2 } ) : ( 3 + 5 ^ { 2 } - 11 \times 2 ) + [ ( 37 - 5 ^ { 2 } ) ^ { 2 } : 3 ^ { 2 } - ( 5 ^ { 2 } - 4 ^ { 2 } ) ] ^ { 3 } : 7 ^ { 2 } \} + 7 \times 15 ^ { 0 } \)

Calculate the value by following steps: - step0: Calculate: \(\frac{66\left(5\left(2\times 5-2\left(21-5\times 2^{2}\right)^{2}\right)^{2}\right)}{\left(2^{3}\times 10\right)}+\left(\frac{19}{\left(3+2\times 8\right)}\right)^{2}+\left(\frac{\left(2^{2}\times 3^{2}\right)}{\left(3+5^{2}-11\times 2\right)}+\frac{\left(\frac{\left(37-5^{2}\right)^{2}}{3^{2}}-\left(5^{2}-4^{2}\right)\right)^{3}}{7^{2}}\right)+7\times 15^{0}\) - step1: Evaluate the power: \(\frac{66\left(5\left(2\times 5-2\left(21-5\times 2^{2}\right)^{2}\right)^{2}\right)}{\left(2^{3}\times 10\right)}+\left(\frac{19}{\left(3+2\times 8\right)}\right)^{2}+\left(\frac{\left(2^{2}\times 3^{2}\right)}{\left(3+5^{2}-11\times 2\right)}+\frac{\left(\frac{\left(37-5^{2}\right)^{2}}{3^{2}}-\left(5^{2}-4^{2}\right)\right)^{3}}{7^{2}}\right)+7\times 1\) - step2: Remove the parentheses: \(\frac{66\times 5\left(2\times 5-2\left(21-5\times 2^{2}\right)^{2}\right)^{2}}{2^{3}\times 10}+\left(\frac{19}{3+2\times 8}\right)^{2}+\left(\frac{2^{2}\times 3^{2}}{3+5^{2}-11\times 2}+\frac{\left(\frac{\left(37-5^{2}\right)^{2}}{3^{2}}-\left(5^{2}-4^{2}\right)\right)^{3}}{7^{2}}\right)+7\times 1\) - step3: Multiply the terms: \(\frac{66\times 5\left(2\times 5-2\left(21-20\right)^{2}\right)^{2}}{2^{3}\times 10}+\left(\frac{19}{3+2\times 8}\right)^{2}+\left(\frac{2^{2}\times 3^{2}}{3+5^{2}-11\times 2}+\frac{\left(\frac{\left(37-5^{2}\right)^{2}}{3^{2}}-\left(5^{2}-4^{2}\right)\right)^{3}}{7^{2}}\right)+7\times 1\) - step4: Subtract the numbers: \(\frac{66\times 5\left(2\times 5-2\times 1^{2}\right)^{2}}{2^{3}\times 10}+\left(\frac{19}{3+2\times 8}\right)^{2}+\left(\frac{2^{2}\times 3^{2}}{3+5^{2}-11\times 2}+\frac{\left(\frac{\left(37-5^{2}\right)^{2}}{3^{2}}-\left(5^{2}-4^{2}\right)\right)^{3}}{7^{2}}\right)+7\times 1\) - step5: Evaluate the power: \(\frac{66\times 5\left(2\times 5-2\times 1\right)^{2}}{2^{3}\times 10}+\left(\frac{19}{3+2\times 8}\right)^{2}+\left(\frac{2^{2}\times 3^{2}}{3+5^{2}-11\times 2}+\frac{\left(\frac{\left(37-5^{2}\right)^{2}}{3^{2}}-\left(5^{2}-4^{2}\right)\right)^{3}}{7^{2}}\right)+7\times 1\) - step6: Multiply the numbers: \(\frac{66\times 5\left(10-2\times 1\right)^{2}}{2^{3}\times 10}+\left(\frac{19}{3+2\times 8}\right)^{2}+\left(\frac{2^{2}\times 3^{2}}{3+5^{2}-11\times 2}+\frac{\left(\frac{\left(37-5^{2}\right)^{2}}{3^{2}}-\left(5^{2}-4^{2}\right)\right)^{3}}{7^{2}}\right)+7\times 1\) - step7: Multiply: \(\frac{66\times 5\left(10-2\right)^{2}}{2^{3}\times 10}+\left(\frac{19}{3+2\times 8}\right)^{2}+\left(\frac{2^{2}\times 3^{2}}{3+5^{2}-11\times 2}+\frac{\left(\frac{\left(37-5^{2}\right)^{2}}{3^{2}}-\left(5^{2}-4^{2}\right)\right)^{3}}{7^{2}}\right)+7\times 1\) - step8: Subtract the numbers: \(\frac{66\times 5\times 8^{2}}{2^{3}\times 10}+\left(\frac{19}{3+2\times 8}\right)^{2}+\left(\frac{2^{2}\times 3^{2}}{3+5^{2}-11\times 2}+\frac{\left(\frac{\left(37-5^{2}\right)^{2}}{3^{2}}-\left(5^{2}-4^{2}\right)\right)^{3}}{7^{2}}\right)+7\times 1\) - step9: Multiply the numbers: \(\frac{66\times 5\times 8^{2}}{2^{3}\times 10}+\left(\frac{19}{3+16}\right)^{2}+\left(\frac{2^{2}\times 3^{2}}{3+5^{2}-11\times 2}+\frac{\left(\frac{\left(37-5^{2}\right)^{2}}{3^{2}}-\left(5^{2}-4^{2}\right)\right)^{3}}{7^{2}}\right)+7\times 1\) - step10: Add the numbers: \(\frac{66\times 5\times 8^{2}}{2^{3}\times 10}+\left(\frac{19}{19}\right)^{2}+\left(\frac{2^{2}\times 3^{2}}{3+5^{2}-11\times 2}+\frac{\left(\frac{\left(37-5^{2}\right)^{2}}{3^{2}}-\left(5^{2}-4^{2}\right)\right)^{3}}{7^{2}}\right)+7\times 1\) - step11: Divide the terms: \(\frac{66\times 5\times 8^{2}}{2^{3}\times 10}+1^{2}+\left(\frac{2^{2}\times 3^{2}}{3+5^{2}-11\times 2}+\frac{\left(\frac{\left(37-5^{2}\right)^{2}}{3^{2}}-\left(5^{2}-4^{2}\right)\right)^{3}}{7^{2}}\right)+7\times 1\) - step12: Subtract the numbers: \(\frac{66\times 5\times 8^{2}}{2^{3}\times 10}+1^{2}+\left(\frac{2^{2}\times 3^{2}}{3+5^{2}-11\times 2}+\frac{\left(\frac{12^{2}}{3^{2}}-\left(5^{2}-4^{2}\right)\right)^{3}}{7^{2}}\right)+7\times 1\) - step13: Subtract the numbers: \(\frac{66\times 5\times 8^{2}}{2^{3}\times 10}+1^{2}+\left(\frac{2^{2}\times 3^{2}}{3+5^{2}-11\times 2}+\frac{\left(\frac{12^{2}}{3^{2}}-9\right)^{3}}{7^{2}}\right)+7\times 1\) - step14: Divide the terms: \(\frac{66\times 5\times 8^{2}}{2^{3}\times 10}+1^{2}+\left(\frac{2^{2}\times 3^{2}}{3+5^{2}-11\times 2}+\frac{\left(4^{2}-9\right)^{3}}{7^{2}}\right)+7\times 1\) - step15: Subtract the numbers: \(\frac{66\times 5\times 8^{2}}{2^{3}\times 10}+1^{2}+\left(\frac{2^{2}\times 3^{2}}{3+5^{2}-11\times 2}+\frac{7^{3}}{7^{2}}\right)+7\times 1\) - step16: Multiply by \(a^{-n}:\) \(\frac{66\times 5\times 8^{2}}{2^{3}\times 10}+1^{2}+\left(\frac{2^{2}\times 3^{2}}{3+5^{2}-11\times 2}+7^{3}\times 7^{-2}\right)+7\times 1\) - step17: Multiply the numbers: \(\frac{66\times 5\times 8^{2}}{2^{3}\times 10}+1^{2}+\left(\frac{2^{2}\times 3^{2}}{3+5^{2}-22}+7^{3}\times 7^{-2}\right)+7\times 1\) - step18: Multiply the numbers: \(\frac{66\times 5\times 8^{2}}{2^{3}\times 10}+1^{2}+\left(\frac{6^{2}}{3+5^{2}-22}+7^{3}\times 7^{-2}\right)+7\times 1\) - step19: Calculate: \(\frac{66\times 5\times 8^{2}}{2^{3}\times 10}+1^{2}+\left(\frac{6^{2}}{6}+7^{3}\times 7^{-2}\right)+7\times 1\) - step20: Reduce the fraction: \(\frac{66\times 5\times 8^{2}}{2^{3}\times 10}+1^{2}+\left(6+7^{3}\times 7^{-2}\right)+7\times 1\) - step21: Multiply the numbers: \(\frac{66\times 5\times 8^{2}}{2^{3}\times 10}+1^{2}+\left(6+7\right)+7\times 1\) - step22: Add the numbers: \(\frac{66\times 5\times 8^{2}}{2^{3}\times 10}+1^{2}+13+7\times 1\) - step23: Multiply the terms: \(\frac{330\times 8^{2}}{2^{3}\times 10}+1^{2}+13+7\times 1\) - step24: Reduce the fraction: \(33\times 2^{3}+1^{2}+13+7\times 1\) - step25: Evaluate the power: \(33\times 2^{3}+1+13+7\times 1\) - step26: Multiply the terms: \(264+1+13+7\times 1\) - step27: Multiply: \(264+1+13+7\) - step28: Add the numbers: \(285\) Il risultato dell'espressione matematica è \( 285 \). Se hai bisogno di ulteriori spiegazioni o di un altro calcolo, fammelo sapere!