Question

If ${\left[{\left\{\right(\frac{1}{7}{)}^{-2}\}}^{\frac{1}{3}}\right]}^{\frac{1}{4}}=7^m$ then find the value of m.

Answer 1

${\left[{\left\{\right(\frac{1}{7}{)}^{-2}\}}^{\frac{1}{3}}\right]}^{\frac{1}{4}}=7^m{\left[{\left\{\right(7^{}{)}^{-2}\}}^{-\frac{1}{3}}\right]}^{\frac{1}{4}}=7^m{\left[{\left\{7^2\right\}}^{-\frac{1}{3}}\right]}^{\frac{1}{4}}=7^m(7^{\frac{-2}{3}}{)}^{\frac{1}{4}}=7^{\frac{-1}{6}}m=\frac{-1}{6}$