Question

${\left(\frac{5^{-1}\times 7^2}{5^2\times 7^4}\right)}^{\frac{7}{2}}\times {\left(\frac{5^{-2}\times 7^3}{5^3\times 7^{-5}}\right)}^{\frac{-5}{2}}$

Answer 1

${\left(\frac{5^{-1}\times 7^2}{5^2\times 7^4}\right)}^{\frac{7}{2}}\times {\left(\frac{5^{-2}\times 7^3}{5^3\times 7^{-5}}\right)}^{-\frac{5}{2}}={(5^{-3}\times 7^{-2})}^{\frac{7}{2}}\times {(5^{-5}\times 7^{-8})}^{-\frac{5}{2}}=5^{-\frac{21}{2}}\times 7^{-7}\times 5^{\frac{25}{2}}\times 7^{20}=5^{-\frac{21}{2}+\frac{25}{2}}\times 7^{-7+20}=5^2\times 7^{13}$}$