Question

(( (5^(m+1)^3)*(1/2)^-(3m))/10^(3m))^(1/3)=?

Answer 1

$\left(\frac{(5^{m+1})^3\left(\frac{1}{2}\right)^{-3m} }{10^{3m}}\right) ^{\frac{1}{3}}=\frac{\left((5^{m+1})^3\right)^{\frac{1}{3}} \left(\left(\frac{1}{2}\right)^{-3m} \right)^{\frac{1}{3}} }{\left(10^{3m}\right) ^{\frac{1}{3}}} =\frac{5^{m+1}\left(\frac{1}{2}\right)^{-m} }{10^m}=\\\\\frac{5\cdot5^{m}\cdot2^{m} }{10^m}=\frac{5\cdot(5\cdot2)^{m} }{10^m}=\frac{5\cdot10^{m}}{10^m}=5$