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\left(\frac{4}{9}-\left(\frac{8}{9}+\frac{8}{3}\right)+\left(\frac{7}{3}\right)^{2}\right)|\left(\frac{1}{7}\right)^{2}+\frac{4}{7}-1-\left(\frac{2}{7}\right)^{2}|
Calculate \frac{2}{3} to the power of 2 and get \frac{4}{9}.
\left(\frac{4}{9}-\left(\frac{8}{9}+\frac{24}{9}\right)+\left(\frac{7}{3}\right)^{2}\right)|\left(\frac{1}{7}\right)^{2}+\frac{4}{7}-1-\left(\frac{2}{7}\right)^{2}|
Least common multiple of 9 and 3 is 9. Convert \frac{8}{9} and \frac{8}{3} to fractions with denominator 9.
\left(\frac{4}{9}-\frac{8+24}{9}+\left(\frac{7}{3}\right)^{2}\right)|\left(\frac{1}{7}\right)^{2}+\frac{4}{7}-1-\left(\frac{2}{7}\right)^{2}|
Since \frac{8}{9} and \frac{24}{9} have the same denominator, add them by adding their numerators.
\left(\frac{4}{9}-\frac{32}{9}+\left(\frac{7}{3}\right)^{2}\right)|\left(\frac{1}{7}\right)^{2}+\frac{4}{7}-1-\left(\frac{2}{7}\right)^{2}|
Add 8 and 24 to get 32.
\left(\frac{4-32}{9}+\left(\frac{7}{3}\right)^{2}\right)|\left(\frac{1}{7}\right)^{2}+\frac{4}{7}-1-\left(\frac{2}{7}\right)^{2}|
Since \frac{4}{9} and \frac{32}{9} have the same denominator, subtract them by subtracting their numerators.
\left(-\frac{28}{9}+\left(\frac{7}{3}\right)^{2}\right)|\left(\frac{1}{7}\right)^{2}+\frac{4}{7}-1-\left(\frac{2}{7}\right)^{2}|
Subtract 32 from 4 to get -28.
\left(-\frac{28}{9}+\frac{49}{9}\right)|\left(\frac{1}{7}\right)^{2}+\frac{4}{7}-1-\left(\frac{2}{7}\right)^{2}|
Calculate \frac{7}{3} to the power of 2 and get \frac{49}{9}.
\frac{-28+49}{9}|\left(\frac{1}{7}\right)^{2}+\frac{4}{7}-1-\left(\frac{2}{7}\right)^{2}|
Since -\frac{28}{9} and \frac{49}{9} have the same denominator, add them by adding their numerators.
\frac{21}{9}|\left(\frac{1}{7}\right)^{2}+\frac{4}{7}-1-\left(\frac{2}{7}\right)^{2}|
Add -28 and 49 to get 21.
\frac{7}{3}|\left(\frac{1}{7}\right)^{2}+\frac{4}{7}-1-\left(\frac{2}{7}\right)^{2}|
Reduce the fraction \frac{21}{9} to lowest terms by extracting and canceling out 3.
\frac{7}{3}|\frac{1}{49}+\frac{4}{7}-1-\left(\frac{2}{7}\right)^{2}|
Calculate \frac{1}{7} to the power of 2 and get \frac{1}{49}.
\frac{7}{3}|\frac{1}{49}+\frac{28}{49}-1-\left(\frac{2}{7}\right)^{2}|
Least common multiple of 49 and 7 is 49. Convert \frac{1}{49} and \frac{4}{7} to fractions with denominator 49.
\frac{7}{3}|\frac{1+28}{49}-1-\left(\frac{2}{7}\right)^{2}|
Since \frac{1}{49} and \frac{28}{49} have the same denominator, add them by adding their numerators.
\frac{7}{3}|\frac{29}{49}-1-\left(\frac{2}{7}\right)^{2}|
Add 1 and 28 to get 29.
\frac{7}{3}|\frac{29}{49}-\frac{49}{49}-\left(\frac{2}{7}\right)^{2}|
Convert 1 to fraction \frac{49}{49}.
\frac{7}{3}|\frac{29-49}{49}-\left(\frac{2}{7}\right)^{2}|
Since \frac{29}{49} and \frac{49}{49} have the same denominator, subtract them by subtracting their numerators.
\frac{7}{3}|-\frac{20}{49}-\left(\frac{2}{7}\right)^{2}|
Subtract 49 from 29 to get -20.
\frac{7}{3}|-\frac{20}{49}-\frac{4}{49}|
Calculate \frac{2}{7} to the power of 2 and get \frac{4}{49}.
\frac{7}{3}|\frac{-20-4}{49}|
Since -\frac{20}{49} and \frac{4}{49} have the same denominator, subtract them by subtracting their numerators.
\frac{7}{3}|-\frac{24}{49}|
Subtract 4 from -20 to get -24.
\frac{7}{3}\times \frac{24}{49}
The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of -\frac{24}{49} is \frac{24}{49}.
\frac{7\times 24}{3\times 49}
Multiply \frac{7}{3} times \frac{24}{49} by multiplying numerator times numerator and denominator times denominator.
\frac{168}{147}
Do the multiplications in the fraction \frac{7\times 24}{3\times 49}.
\frac{8}{7}
Reduce the fraction \frac{168}{147} to lowest terms by extracting and canceling out 21.