Question

please help me do this.. explain step by step. ​

Answer 1

Answer:

$\sf \bigg( \dfrac{81}{16} \bigg)^{\dfrac{-3}{4}}\times \bigg[ \bigg( \dfrac{25}{9} \bigg)^{\dfrac{-3}{2}} \div \bigg( \dfrac{5}{2} \bigg)^{-3} \bigg] = 1$

Step-by-step explanation:

$\implies \sf \bigg( \dfrac{81}{16} \bigg)^{\dfrac{-3}{4}}\times \bigg[ \bigg( \dfrac{25}{9} \bigg)^{\dfrac{-3}{2}} \div \bigg( \dfrac{5}{2} \bigg)^{-3} \bigg]$

:$\implies \sf \bigg( \dfrac{81}{16} \bigg)^{\dfrac{-3}{4}}\times \bigg[ \bigg( \dfrac{25}{9} \bigg)^{\dfrac{-3}{2}} \div \bigg( \dfrac{2}{5} \bigg)^{3} \bigg]$

:$\implies \sf \bigg( \dfrac{16}{81} \bigg)^{\dfrac{3}{4}} \times \bigg[ \bigg( \dfrac{9}{25} \bigg)^{\dfrac{3}{2}} \div \dfrac{2^3}{5^3} \bigg]$

:$\implies \sf \dfrac{16^{\dfrac{3}{4}}}{81^{\dfrac{3}{4}}} \times \bigg[ \dfrac{9^{\dfrac{3}{2}}}{25^{\dfrac{3}{2}}} \times \dfrac{5^3}{2^3} \bigg]$

:$\implies \sf \dfrac{2^3}{3^3} \times \bigg( \dfrac{3^3}{5^3} \times \dfrac{5^3}{8} \bigg)$

:$\implies \sf \dfrac{2^3}{3^3} \bigg( 27 \times \dfrac{1}{8} \bigg)$

:$\implies \sf \dfrac{2^3}{3^3} \times \dfrac{27}{8}$

:$\implies \sf \dfrac{2^3}{3^3} \times \dfrac{3^3}{2^3}$

:$\implies \sf \dfrac{\cancel{2^3}}{\cancel{3^3}} \times \dfrac{\cancel{3^3}}{\cancel{2^3}}$

:$\implies \sf 1$