Solve [(4/7)^3-(1/4+4/3)]^2

$$[ ( \frac { 4 } { 7 } ) ^ { 3 } - ( \frac { 1 } { 4 } + \frac { 4 } { 3 } ) ] ^ { 2 }$$

Evaluate

$$\frac{33051001}{16941456}\approx 1.950894953$$

Solution Steps

Calculate \frac{4}{7} to the power of 3 and get \frac{64}{343}.

$$\left(\frac{64}{343}-\left(\frac{1}{4}+\frac{4}{3}\right)\right)^{2}$$

Add \frac{1}{4} and \frac{4}{3} to get \frac{19}{12}.

$$\left(\frac{64}{343}-\frac{19}{12}\right)^{2}$$

Subtract \frac{19}{12} from \frac{64}{343} to get -\frac{5749}{4116}.

$$\left(-\frac{5749}{4116}\right)^{2}$$

Calculate -\frac{5749}{4116} to the power of 2 and get \frac{33051001}{16941456}.

$$\frac{33051001}{16941456}$$

Factor

$$\frac{5749 ^ {2}}{2 ^ {4} \cdot 3 ^ {2} \cdot 7 ^ {6}} = 1\frac{16109545}{16941456} = 1.9508949525943933$$