Solve frac{sqrt{4}}{3}-2/3*[(2/7)]^2*2/7*(5^2/6*frac{2^2}{5}-1)-frac{1}{6}]+3=

$$\frac { \sqrt { 4 } } { 3 } - \frac { 2 } { 3 } \times [ ( \frac { 2 } { 7 } ) ] ^ { 2 } \cdot \frac { 2 } { 7 } \times ( \frac { 5 ^ { 2 } } { 6 } \times \frac { 2 ^ { 2 } } { 5 } - 1 ) - \frac { 1 } { 6 } ] + 3 =$$

Evaluate

$$\frac{409}{882}\approx 0.463718821$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$\frac{\sqrt{4}}{3}-\frac{2}{3}\times \left(\frac{2}{7}\right)^{3}\left(\frac{5^{2}}{6}\times \frac{2^{2}}{5}-1\right)-\frac{1}{6}$$

Calculate the square root of 4 and get 2.

$$\frac{2}{3}-\frac{2}{3}\times \left(\frac{2}{7}\right)^{3}\left(\frac{5^{2}}{6}\times \frac{2^{2}}{5}-1\right)-\frac{1}{6}$$

Calculate \frac{2}{7} to the power of 3 and get \frac{8}{343}.

$$\frac{2}{3}-\frac{2}{3}\times \frac{8}{343}\left(\frac{5^{2}}{6}\times \frac{2^{2}}{5}-1\right)-\frac{1}{6}$$

Multiply \frac{2}{3} times \frac{8}{343} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2}{3}-\frac{2\times 8}{3\times 343}\left(\frac{5^{2}}{6}\times \frac{2^{2}}{5}-1\right)-\frac{1}{6}$$

Do the multiplications in the fraction \frac{2\times 8}{3\times 343}.

$$\frac{2}{3}-\frac{16}{1029}\left(\frac{5^{2}}{6}\times \frac{2^{2}}{5}-1\right)-\frac{1}{6}$$

Calculate 5 to the power of 2 and get 25.

$$\frac{2}{3}-\frac{16}{1029}\left(\frac{25}{6}\times \frac{2^{2}}{5}-1\right)-\frac{1}{6}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{2}{3}-\frac{16}{1029}\left(\frac{25}{6}\times \frac{4}{5}-1\right)-\frac{1}{6}$$

Multiply \frac{25}{6} times \frac{4}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2}{3}-\frac{16}{1029}\left(\frac{25\times 4}{6\times 5}-1\right)-\frac{1}{6}$$

Do the multiplications in the fraction \frac{25\times 4}{6\times 5}.

$$\frac{2}{3}-\frac{16}{1029}\left(\frac{100}{30}-1\right)-\frac{1}{6}$$

Reduce the fraction \frac{100}{30} to lowest terms by extracting and canceling out 10.

$$\frac{2}{3}-\frac{16}{1029}\left(\frac{10}{3}-1\right)-\frac{1}{6}$$

Convert 1 to fraction \frac{3}{3}.

$$\frac{2}{3}-\frac{16}{1029}\left(\frac{10}{3}-\frac{3}{3}\right)-\frac{1}{6}$$

Since \frac{10}{3} and \frac{3}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2}{3}-\frac{16}{1029}\times \frac{10-3}{3}-\frac{1}{6}$$

Subtract 3 from 10 to get 7.

$$\frac{2}{3}-\frac{16}{1029}\times \frac{7}{3}-\frac{1}{6}$$

Multiply \frac{16}{1029} times \frac{7}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2}{3}-\frac{16\times 7}{1029\times 3}-\frac{1}{6}$$

Do the multiplications in the fraction \frac{16\times 7}{1029\times 3}.

$$\frac{2}{3}-\frac{112}{3087}-\frac{1}{6}$$

Reduce the fraction \frac{112}{3087} to lowest terms by extracting and canceling out 7.

$$\frac{2}{3}-\frac{16}{441}-\frac{1}{6}$$

Least common multiple of 3 and 441 is 441. Convert \frac{2}{3} and \frac{16}{441} to fractions with denominator 441.

$$\frac{294}{441}-\frac{16}{441}-\frac{1}{6}$$

Since \frac{294}{441} and \frac{16}{441} have the same denominator, subtract them by subtracting their numerators.

$$\frac{294-16}{441}-\frac{1}{6}$$

Subtract 16 from 294 to get 278.

$$\frac{278}{441}-\frac{1}{6}$$

Least common multiple of 441 and 6 is 882. Convert \frac{278}{441} and \frac{1}{6} to fractions with denominator 882.

$$\frac{556}{882}-\frac{147}{882}$$

Since \frac{556}{882} and \frac{147}{882} have the same denominator, subtract them by subtracting their numerators.

$$\frac{556-147}{882}$$

Subtract 147 from 556 to get 409.

$$\frac{409}{882}$$

Factor

$$\frac{409}{2 \cdot 3 ^ {2} \cdot 7 ^ {2}} = 0.463718820861678$$