Resol 2^-1[(5/3)^4+(3/5)^-2]div17/9

$$2 ^ { - 1 } [ ( \frac { 5 } { 3 } ) ^ { 4 } + ( \frac { 3 } { 5 } ) ^ { - 2 } ] \div \frac { 17 } { 9 }$$

Calcula

$$\frac{25}{9}\approx 2,777777778$$

Passos de solució

Calculeu 2 elevat a -1 per obtenir \frac{1}{2}.

$$\frac{\frac{1}{2}\left(\left(\frac{5}{3}\right)^{4}+\left(\frac{3}{5}\right)^{-2}\right)}{\frac{17}{9}}$$

Calculeu \frac{5}{3} elevat a 4 per obtenir \frac{625}{81}.

$$\frac{\frac{1}{2}\left(\frac{625}{81}+\left(\frac{3}{5}\right)^{-2}\right)}{\frac{17}{9}}$$

Calculeu \frac{3}{5} elevat a -2 per obtenir \frac{25}{9}.

$$\frac{\frac{1}{2}\left(\frac{625}{81}+\frac{25}{9}\right)}{\frac{17}{9}}$$

Sumeu \frac{625}{81} més \frac{25}{9} per obtenir \frac{850}{81}.

$$\frac{\frac{1}{2}\times \frac{850}{81}}{\frac{17}{9}}$$

Multipliqueu \frac{1}{2} per \frac{850}{81} per obtenir \frac{425}{81}.

$$\frac{\frac{425}{81}}{\frac{17}{9}}$$

Dividiu \frac{425}{81} per \frac{17}{9} multiplicant \frac{425}{81} pel recíproc de \frac{17}{9}.

$$\frac{425}{81}\times \frac{9}{17}$$

Multipliqueu \frac{425}{81} per \frac{9}{17} per obtenir \frac{25}{9}.

$$\frac{25}{9}$$

Factoritzar

$$\frac{5 ^ {2}}{3 ^ {2}} = 2\frac{7}{9} = 2,7777777777777777$$