Solve {left(3/2right)}^2-{left(1/2right)}^3+{left(1/7right)}^2*{left(2/7right)}^2

$${ \left( \frac{ 3 }{ 2 } \right) }^{ 2 } - { \left( \frac{ 1 }{ 2 } \right) }^{ 3 } + { \left( \frac{ 1 }{ 7 } \right) }^{ 2 } \times { \left( \frac{ 2 }{ 7 } \right) }^{ 2 }$$

Evaluate

$$\frac{40849}{19208}\approx 2.126665973$$

Solution Steps

Calculate \frac{3}{2} to the power of 2 and get \frac{9}{4}.

$$\frac{9}{4}-\left(\frac{1}{2}\right)^{3}+\left(\frac{1}{7}\right)^{2}\times \left(\frac{2}{7}\right)^{2}$$

Calculate \frac{1}{2} to the power of 3 and get \frac{1}{8}.

$$\frac{9}{4}-\frac{1}{8}+\left(\frac{1}{7}\right)^{2}\times \left(\frac{2}{7}\right)^{2}$$

Least common multiple of 4 and 8 is 8. Convert \frac{9}{4} and \frac{1}{8} to fractions with denominator 8.

$$\frac{18}{8}-\frac{1}{8}+\left(\frac{1}{7}\right)^{2}\times \left(\frac{2}{7}\right)^{2}$$

Since \frac{18}{8} and \frac{1}{8} have the same denominator, subtract them by subtracting their numerators.

$$\frac{18-1}{8}+\left(\frac{1}{7}\right)^{2}\times \left(\frac{2}{7}\right)^{2}$$

Subtract 1 from 18 to get 17.

$$\frac{17}{8}+\left(\frac{1}{7}\right)^{2}\times \left(\frac{2}{7}\right)^{2}$$

Calculate \frac{1}{7} to the power of 2 and get \frac{1}{49}.

$$\frac{17}{8}+\frac{1}{49}\times \left(\frac{2}{7}\right)^{2}$$

Calculate \frac{2}{7} to the power of 2 and get \frac{4}{49}.

$$\frac{17}{8}+\frac{1}{49}\times \frac{4}{49}$$

Multiply \frac{1}{49} times \frac{4}{49} by multiplying numerator times numerator and denominator times denominator.

$$\frac{17}{8}+\frac{1\times 4}{49\times 49}$$

Do the multiplications in the fraction \frac{1\times 4}{49\times 49}.

$$\frac{17}{8}+\frac{4}{2401}$$

Least common multiple of 8 and 2401 is 19208. Convert \frac{17}{8} and \frac{4}{2401} to fractions with denominator 19208.

$$\frac{40817}{19208}+\frac{32}{19208}$$

Since \frac{40817}{19208} and \frac{32}{19208} have the same denominator, add them by adding their numerators.

$$\frac{40817+32}{19208}$$

Add 40817 and 32 to get 40849.

$$\frac{40849}{19208}$$

Factor

$$\frac{40849}{2 ^ {3} \cdot 7 ^ {4}} = 2\frac{2433}{19208} = 2.1266659725114536$$