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\(\frac{14^{16}\times21^{32}\times35^{48}}{10^{16}\times35^{32}\times7^{96}}\)
\(=\frac{\left(2\times7\right)^{16}\times\left(3\times7\right)^{32}\times\left(5\times7\right)^{48}}{\left(2\times5\right)^{16}\times\left(5\times7\right)^{32}\times7^{96}}\)
\(=\frac{2^{16}\times7^{16}\times3^{32}\times7^{32}\times5^{48}\times7^{48}}{2^{16}\times5^{16}\times5^{32}\times7^{32}\times7^{96}}=\frac{2^{16}+7^{96}+3^{32}+5^{48}}{2^{16}\times5^{48}\times7^{32}\times7^{96}}\)
\(=\frac{3^{32}}{7^{32}}=\left(\frac{3}{7}\right)^{32}\)