Solve [(3/7)^8*(7/9)^5]^1/3

$$[ ( \frac { 3 } { 7 } ) ^ { 8 } \cdot ( \frac { 7 } { 9 } ) ^ { 5 } ] ^ { 1 / 3 }$$

Evaluate

$$\frac{9^{\frac{2}{3}}}{63}\approx 0.068678551$$

Solution Steps

Calculate \frac{3}{7} to the power of 8 and get \frac{6561}{5764801}.

$$\left(\frac{6561}{5764801}\times \left(\frac{7}{9}\right)^{5}\right)^{\frac{1}{3}}$$

Calculate \frac{7}{9} to the power of 5 and get \frac{16807}{59049}.

$$\left(\frac{6561}{5764801}\times \frac{16807}{59049}\right)^{\frac{1}{3}}$$

Multiply \frac{6561}{5764801} and \frac{16807}{59049} to get \frac{1}{3087}.

$$\left(\frac{1}{3087}\right)^{\frac{1}{3}}$$