Discussion Forum

Number of prime numbers in $\frac{6^{12}\times 35^{28}\times 15^{16}}{14^{12}\times 21^{11}}is:$

Answer:

Explanation:

$\frac{6^{12}\times 35^{28}\times 15^{16}}{14^{12}\times 21^{11}}=$ $=\frac{\left(2\times 3\right)^{12}\times \left(5\times7\right)^{28}\times \left(3\times 5\right)^{16}}{\left(2\times 7\right)^{12}\times \left(3 \times 7\right)^{11}}$ $=\frac{2^{12}\times 3^{12}\times 5^{28}\times 7^{28}\times 3^{16}\times 5^{16}}{2^{12}\times 7^{12}\times 3^{11}\times 7^{11}}$ $=2^{\left(12-12\right)}\times 3^{\left(12+16-11\right)}\times5^{\left(28+16\right)}\times7^{\left(28-12-11\right)}$ $=2^{0} \times3^{17} \times5^{44} \times7^{-5}$ $=\frac{3^{17}\times 5^{44} }{7^{5}}$ Number of prime factors = 17 + 44 + 5 = 66.