Solve (-8/3)^2+(-32/9)^2

$$( - \frac { 8 } { 3 } ) ^ { 2 } + ( - \frac { 32 } { 9 } ) ^ { 2 }$$

Evaluate

$$\frac{1600}{81}\approx 19.75308642$$

Solution Steps

Calculate -\frac{8}{3} to the power of 2 and get \frac{64}{9}.

$$\frac{64}{9}+\left(-\frac{32}{9}\right)^{2}$$

Calculate -\frac{32}{9} to the power of 2 and get \frac{1024}{81}.

$$\frac{64}{9}+\frac{1024}{81}$$

Least common multiple of 9 and 81 is 81. Convert \frac{64}{9} and \frac{1024}{81} to fractions with denominator 81.

$$\frac{576}{81}+\frac{1024}{81}$$

Since \frac{576}{81} and \frac{1024}{81} have the same denominator, add them by adding their numerators.

$$\frac{576+1024}{81}$$

Add 576 and 1024 to get 1600.

$$\frac{1600}{81}$$

Factor

$$\frac{2 ^ {6} \cdot 5 ^ {2}}{3 ^ {4}} = 19\frac{61}{81} = 19.753086419753085$$