Solve 2/3div-3/2+(1+16/27)*(1/4+frac{7}{8})-(frac{3^12}{4}divfrac{3^10}{4})=-frac{59}{48}

$$\frac{ 2 }{ 3 } \div - \frac{ 3 }{ 2 } +(1+ \frac{ 16 }{ 27 } ) \times ( \frac{ 1 }{ 4 } + \frac{ 7 }{ 8 } )-( \frac{ { 3 }^{ 12 } }{ 4 } \div \frac{ { 3 }^{ 10 } }{ 4 } )=- \frac{ 59 }{ 48 }$$

Verify

Solution Steps

Divide \frac{2}{3} by -\frac{3}{2} by multiplying \frac{2}{3} by the reciprocal of -\frac{3}{2}.

$$\frac{2}{3}\left(-\frac{2}{3}\right)+\left(1+\frac{16}{27}\right)\left(\frac{1}{4}+\frac{7}{8}\right)-\frac{\frac{3^{12}}{4}}{\frac{3^{10}}{4}}=-\frac{59}{48}$$

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

$$\frac{2\left(-2\right)}{3\times 3}+\left(1+\frac{16}{27}\right)\left(\frac{1}{4}+\frac{7}{8}\right)-\frac{\frac{3^{12}}{4}}{\frac{3^{10}}{4}}=-\frac{59}{48}$$

Do the multiplications in the fraction \frac{2\left(-2\right)}{3\times 3}.

$$\frac{-4}{9}+\left(1+\frac{16}{27}\right)\left(\frac{1}{4}+\frac{7}{8}\right)-\frac{\frac{3^{12}}{4}}{\frac{3^{10}}{4}}=-\frac{59}{48}$$

Fraction \frac{-4}{9} can be rewritten as -\frac{4}{9} by extracting the negative sign.

$$-\frac{4}{9}+\left(1+\frac{16}{27}\right)\left(\frac{1}{4}+\frac{7}{8}\right)-\frac{\frac{3^{12}}{4}}{\frac{3^{10}}{4}}=-\frac{59}{48}$$

Convert 1 to fraction \frac{27}{27}.

$$-\frac{4}{9}+\left(\frac{27}{27}+\frac{16}{27}\right)\left(\frac{1}{4}+\frac{7}{8}\right)-\frac{\frac{3^{12}}{4}}{\frac{3^{10}}{4}}=-\frac{59}{48}$$

Since \frac{27}{27} and \frac{16}{27} have the same denominator, add them by adding their numerators.

$$-\frac{4}{9}+\frac{27+16}{27}\left(\frac{1}{4}+\frac{7}{8}\right)-\frac{\frac{3^{12}}{4}}{\frac{3^{10}}{4}}=-\frac{59}{48}$$

Add 27 and 16 to get 43.

$$-\frac{4}{9}+\frac{43}{27}\left(\frac{1}{4}+\frac{7}{8}\right)-\frac{\frac{3^{12}}{4}}{\frac{3^{10}}{4}}=-\frac{59}{48}$$

Least common multiple of 4 and 8 is 8. Convert \frac{1}{4} and \frac{7}{8} to fractions with denominator 8.

$$-\frac{4}{9}+\frac{43}{27}\left(\frac{2}{8}+\frac{7}{8}\right)-\frac{\frac{3^{12}}{4}}{\frac{3^{10}}{4}}=-\frac{59}{48}$$

Since \frac{2}{8} and \frac{7}{8} have the same denominator, add them by adding their numerators.

$$-\frac{4}{9}+\frac{43}{27}\times \frac{2+7}{8}-\frac{\frac{3^{12}}{4}}{\frac{3^{10}}{4}}=-\frac{59}{48}$$

Add 2 and 7 to get 9.

$$-\frac{4}{9}+\frac{43}{27}\times \frac{9}{8}-\frac{\frac{3^{12}}{4}}{\frac{3^{10}}{4}}=-\frac{59}{48}$$

Multiply \frac{43}{27} times \frac{9}{8} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{4}{9}+\frac{43\times 9}{27\times 8}-\frac{\frac{3^{12}}{4}}{\frac{3^{10}}{4}}=-\frac{59}{48}$$

Do the multiplications in the fraction \frac{43\times 9}{27\times 8}.

$$-\frac{4}{9}+\frac{387}{216}-\frac{\frac{3^{12}}{4}}{\frac{3^{10}}{4}}=-\frac{59}{48}$$

Reduce the fraction \frac{387}{216} to lowest terms by extracting and canceling out 9.

$$-\frac{4}{9}+\frac{43}{24}-\frac{\frac{3^{12}}{4}}{\frac{3^{10}}{4}}=-\frac{59}{48}$$

Least common multiple of 9 and 24 is 72. Convert -\frac{4}{9} and \frac{43}{24} to fractions with denominator 72.

$$-\frac{32}{72}+\frac{129}{72}-\frac{\frac{3^{12}}{4}}{\frac{3^{10}}{4}}=-\frac{59}{48}$$

Since -\frac{32}{72} and \frac{129}{72} have the same denominator, add them by adding their numerators.

$$\frac{-32+129}{72}-\frac{\frac{3^{12}}{4}}{\frac{3^{10}}{4}}=-\frac{59}{48}$$

Add -32 and 129 to get 97.

$$\frac{97}{72}-\frac{\frac{3^{12}}{4}}{\frac{3^{10}}{4}}=-\frac{59}{48}$$

Divide \frac{3^{12}}{4} by \frac{3^{10}}{4} by multiplying \frac{3^{12}}{4} by the reciprocal of \frac{3^{10}}{4}.

$$\frac{97}{72}-\frac{3^{12}\times 4}{4\times 3^{10}}=-\frac{59}{48}$$

Cancel out 4\times 3^{10} in both numerator and denominator.

$$\frac{97}{72}-3^{2}=-\frac{59}{48}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{97}{72}-9=-\frac{59}{48}$$

Convert 9 to fraction \frac{648}{72}.

$$\frac{97}{72}-\frac{648}{72}=-\frac{59}{48}$$

Since \frac{97}{72} and \frac{648}{72} have the same denominator, subtract them by subtracting their numerators.

$$\frac{97-648}{72}=-\frac{59}{48}$$

Subtract 648 from 97 to get -551.

$$-\frac{551}{72}=-\frac{59}{48}$$

Least common multiple of 72 and 48 is 144. Convert -\frac{551}{72} and -\frac{59}{48} to fractions with denominator 144.

$$-\frac{1102}{144}=-\frac{177}{144}$$

Compare -\frac{1102}{144} and -\frac{177}{144}.

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