Pasando todo a fracciones:
$$\left(-\frac{34}{10}\right)^2+\frac{1468}{\frac{87}{10}}-\sqrt[3]{\frac{512}{1000}}$$
Después simplificando:
$$\frac{1156}{100}+\frac{14680}{87}-\frac{\sqrt[3]{512}}{\sqrt[3]{1000}}$$
$$\frac{289}{25}+\frac{14680}{87}-\frac{8}{10}$$
$$\frac{289}{25}+\frac{14680}{87}-\frac{4}{5}$$
Sacando $MCM_{(25; 87; 5)}=2175$ pasás todo a
denominador $2175$:
$$\frac{289\times\frac{2175}{25}}{25\times\frac{2175}{25}}+\frac{14680\times\frac{2175}{87}}{87\times\frac{2175}{87}}-\frac{4\times\frac{2175}{5}}{5\times\frac{2175}{5}}$$
$$\frac{25143}{2175}+\frac{367000}{2175}-\frac{1740}{2175}$$
$$\frac{25143+367000-1740}{2175}=\frac{390403}{2175}$$