Solve (3/8-6)^2*(3/8-2)^2*(3/8-3)^2

$$( \frac { 3 } { 8 } - 6 ) ^ { 2 } \cdot ( \frac { 3 } { 8 } - 2 ) ^ { 2 } \cdot ( \frac { 3 } { 8 } - 3 ) ^ { 2 }$$

Evaluate

$$\frac{150921225}{262144}=575.718784332$$

Solution Steps

Subtract 6 from \frac{3}{8} to get -\frac{45}{8}.

$$\left(-\frac{45}{8}\right)^{2}\left(\frac{3}{8}-2\right)^{2}\left(\frac{3}{8}-3\right)^{2}$$

Calculate -\frac{45}{8} to the power of 2 and get \frac{2025}{64}.

$$\frac{2025}{64}\left(\frac{3}{8}-2\right)^{2}\left(\frac{3}{8}-3\right)^{2}$$

Subtract 2 from \frac{3}{8} to get -\frac{13}{8}.

$$\frac{2025}{64}\left(-\frac{13}{8}\right)^{2}\left(\frac{3}{8}-3\right)^{2}$$

Calculate -\frac{13}{8} to the power of 2 and get \frac{169}{64}.

$$\frac{2025}{64}\times \frac{169}{64}\left(\frac{3}{8}-3\right)^{2}$$

Multiply \frac{2025}{64} and \frac{169}{64} to get \frac{342225}{4096}.

$$\frac{342225}{4096}\left(\frac{3}{8}-3\right)^{2}$$

Subtract 3 from \frac{3}{8} to get -\frac{21}{8}.

$$\frac{342225}{4096}\left(-\frac{21}{8}\right)^{2}$$

Calculate -\frac{21}{8} to the power of 2 and get \frac{441}{64}.

$$\frac{342225}{4096}\times \frac{441}{64}$$

Multiply \frac{342225}{4096} and \frac{441}{64} to get \frac{150921225}{262144}.

$$\frac{150921225}{262144}$$

Factor

$$\frac{3 ^ {6} \cdot 5 ^ {2} \cdot 7 ^ {2} \cdot 13 ^ {2}}{2 ^ {18}} = 575\frac{188425}{262144} = 575.7187843322754$$