Question

$${ 2 }^{ 2 } \times { 5 }^{ 2 } \times { 9 }^{ 2 } \sqrt{ 6 \times } { 1 }^{ 2 } { 2 }^{ 2 } { 3 }^{ 2 } { 4 }^{ 2 } { 5 }^{ 2 } { 6 }^{ 2 } { 7 }^{ 2 } { 8 }^{ 2 } { 9 }^{ 2 }$$

Answer

$$106.662334464*10^13*sqrt(6*)$$

Solution


Simplify  \({2}^{2}\)  to  \(4\).
\[4\times {5}^{2}\times {9}^{2}\sqrt{6}\times {1}^{2}\times 4\times {3}^{2}\times {4}^{2}\times {5}^{2}\times {6}^{2}\times {7}^{2}\times {8}^{2}\times {9}^{2}\]
Simplify  \({5}^{2}\)  to  \(25\).
\[4\times 25\times {9}^{2}\sqrt{6}\times {1}^{2}\times 4\times {3}^{2}\times {4}^{2}\times 25\times {6}^{2}\times {7}^{2}\times {8}^{2}\times {9}^{2}\]
Simplify  \({9}^{2}\)  to  \(81\).
\[4\times 25\times 81\sqrt{6}\times {1}^{2}\times 4\times {3}^{2}\times {4}^{2}\times 25\times {6}^{2}\times {7}^{2}\times {8}^{2}\times 81\]
Simplify  \({1}^{2}\)  to  \(1\).
\[4\times 25\times 81\sqrt{6}\times 1\times 4\times {3}^{2}\times {4}^{2}\times 25\times {6}^{2}\times {7}^{2}\times {8}^{2}\times 81\]
Simplify  \({3}^{2}\)  to  \(9\).
\[4\times 25\times 81\sqrt{6}\times 1\times 4\times 9\times {4}^{2}\times 25\times {6}^{2}\times {7}^{2}\times {8}^{2}\times 81\]
Simplify  \({4}^{2}\)  to  \(16\).
\[4\times 25\times 81\sqrt{6}\times 1\times 4\times 9\times 16\times 25\times {6}^{2}\times {7}^{2}\times {8}^{2}\times 81\]
Simplify  \({6}^{2}\)  to  \(36\).
\[4\times 25\times 81\sqrt{6}\times 1\times 4\times 9\times 16\times 25\times 36\times {7}^{2}\times {8}^{2}\times 81\]
Simplify  \({7}^{2}\)  to  \(49\).
\[4\times 25\times 81\sqrt{6}\times 1\times 4\times 9\times 16\times 25\times 36\times 49\times {8}^{2}\times 81\]
Simplify  \({8}^{2}\)  to  \(64\).
\[4\times 25\times 81\sqrt{6}\times 1\times 4\times 9\times 16\times 25\times 36\times 49\times 64\times 81\]
Simplify.
\[106.662334\times {10}^{13}\sqrt{6}\]