Question

para a=3^(-1). 81² e b= 2⁴. 6³. 9², calcule (7)^√ab

Answer 1

$a=3^{-1}.81^{2}\\\\b=2^{4}.6^{3}.9^{2}\\\\\\\\\sqrt[7]{ab}=\\\\=\sqrt[7]{(3^{-1}.81^{2}).(2^{4}.6^{3}.9^{2})}=\\\\=\sqrt[7]{3^{-1}.81^{2}.2^{4}.6^{3}.9^{2}}=\\\\=\sqrt[7]{3^{-1}.(3^{4})^{2}.2^{4}.(3.2)^{3}.(3^{2})^{2}}=\\\\=\sqrt[7]{3^{-1}.3^{4.2}.2^{4}.3^{3}.2^{3}.3^{2.2}}=\\\\=\sqrt[7]{3^{-1}.3^{8}.2^{4}.3^{3}.2^{3}.3^{4}}=\\\\=\sqrt[7]{3^{-1+8+3+4}.2^{4+3}}=\\\\=\sqrt[7]{3^{14}.2^{7}}=\\\\=(3^{14}.2^{7})^{\frac{1}{7}}=\\\\=3^{14.(\frac{1}{7})}.2^{7.\frac{1}{7}}=\\\\=3^{2}.2=\\\\=9.2=\\\\=18$