Question

( 32 ) ^1/ 5 ×(343)^_1/3 × (25)^x ÷(729)^1/3 ×(16)^1/4 ×(49)^_1/2=(5/3)^2 find the value of x

Answer 1

$\frac{ {(32)}^{ \frac{1}{5} } \times {(343)}^{ \frac{1}{3} } \times {25}^{x} }{ {(729)}^{ \frac{1}{3} } \times {(16)}^{ \frac{1}{4} } \times {(49)}^{ \frac{1}{2} } } = {( \frac{5}{3}) }^{2} \\ \frac{ \sqrt[5]{32} \times \sqrt[3]{343} \times {25}^{x} }{ \sqrt[3]{729} \times \sqrt[4]{16} \times \sqrt[2]{49} } = { (\frac{5}{3} )}^{2} \\ \frac{2 \times 7 \times {25}^{x} }{9 \times 2 \times 7} = {( \frac{5}{3}) }^{2} \\ \frac{ {25}^{x} }{9} = { (\frac{5}{3}) }^{2} \\ { (\frac{5}{3} )}^{2x} = { (\frac{5}{3} )}^{2} \\ 2x = 2 \\ x = 1$