$${ 1 }^{ 2 } { 4 }^{ 2 } { 6 }^{ 2 } = { 2 }^{ 2 } { 7 }^{ 2 } { 8 }^{ 2 }$$
$\text{false}$
$$1\times 4^{2}\times 6^{2}=2^{2}\times 7^{2}\times 8^{2}$$
$$1\times 16\times 6^{2}=2^{2}\times 7^{2}\times 8^{2}$$
$$16\times 6^{2}=2^{2}\times 7^{2}\times 8^{2}$$
$$16\times 36=2^{2}\times 7^{2}\times 8^{2}$$
$$576=2^{2}\times 7^{2}\times 8^{2}$$
$$576=4\times 7^{2}\times 8^{2}$$
$$576=4\times 49\times 8^{2}$$
$$576=196\times 8^{2}$$
$$576=196\times 64$$
$$576=12544$$
$$\text{false}$$
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