Solve (-3/2)^3-[3/4*5/(-6)-sqrt{1/4}*frac{2}{sqrt{36}}*3][-frac{9}{4}]

$$( - \frac { 3 } { 2 } ) ^ { 3 } - [ \frac { 3 } { 4 } \cdot \frac { 5 } { ( - 6 ) } - \sqrt { \frac { 1 } { 4 } } \cdot \frac { 2 } { \sqrt { 36 } } \cdot 3 ] [ - \frac { 9 } { 4 } ]$$

Evaluate

$$-\frac{189}{32}=-5.90625$$

Solution Steps

Calculate -\frac{3}{2} to the power of 3 and get -\frac{27}{8}.

$$-\frac{27}{8}-\left(\frac{3}{4}\times \frac{5}{-6}-3\sqrt{\frac{1}{4}}\times \frac{2}{\sqrt{36}}\right)\left(-\frac{9}{4}\right)$$

Fraction \frac{5}{-6} can be rewritten as -\frac{5}{6} by extracting the negative sign.

$$-\frac{27}{8}-\left(\frac{3}{4}\left(-\frac{5}{6}\right)-3\sqrt{\frac{1}{4}}\times \frac{2}{\sqrt{36}}\right)\left(-\frac{9}{4}\right)$$

Multiply \frac{3}{4} times -\frac{5}{6} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{27}{8}-\left(\frac{3\left(-5\right)}{4\times 6}-3\sqrt{\frac{1}{4}}\times \frac{2}{\sqrt{36}}\right)\left(-\frac{9}{4}\right)$$

Do the multiplications in the fraction \frac{3\left(-5\right)}{4\times 6}.

$$-\frac{27}{8}-\left(\frac{-15}{24}-3\sqrt{\frac{1}{4}}\times \frac{2}{\sqrt{36}}\right)\left(-\frac{9}{4}\right)$$

Reduce the fraction \frac{-15}{24} to lowest terms by extracting and canceling out 3.

$$-\frac{27}{8}-\left(-\frac{5}{8}-3\sqrt{\frac{1}{4}}\times \frac{2}{\sqrt{36}}\right)\left(-\frac{9}{4}\right)$$

Rewrite the square root of the division \frac{1}{4} as the division of square roots \frac{\sqrt{1}}{\sqrt{4}}. Take the square root of both numerator and denominator.

$$-\frac{27}{8}-\left(-\frac{5}{8}-3\times \frac{1}{2}\times \frac{2}{\sqrt{36}}\right)\left(-\frac{9}{4}\right)$$

Multiply 3 and \frac{1}{2} to get \frac{3}{2}.

$$-\frac{27}{8}-\left(-\frac{5}{8}-\frac{3}{2}\times \frac{2}{\sqrt{36}}\right)\left(-\frac{9}{4}\right)$$

Calculate the square root of 36 and get 6.

$$-\frac{27}{8}-\left(-\frac{5}{8}-\frac{3}{2}\times \frac{2}{6}\right)\left(-\frac{9}{4}\right)$$

Reduce the fraction \frac{2}{6} to lowest terms by extracting and canceling out 2.

$$-\frac{27}{8}-\left(-\frac{5}{8}-\frac{3}{2}\times \frac{1}{3}\right)\left(-\frac{9}{4}\right)$$

Multiply \frac{3}{2} times \frac{1}{3} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{27}{8}-\left(-\frac{5}{8}-\frac{3\times 1}{2\times 3}\right)\left(-\frac{9}{4}\right)$$

Cancel out 3 in both numerator and denominator.

$$-\frac{27}{8}-\left(-\frac{5}{8}-\frac{1}{2}\right)\left(-\frac{9}{4}\right)$$

Least common multiple of 8 and 2 is 8. Convert -\frac{5}{8} and \frac{1}{2} to fractions with denominator 8.

$$-\frac{27}{8}-\left(-\frac{5}{8}-\frac{4}{8}\right)\left(-\frac{9}{4}\right)$$

Since -\frac{5}{8} and \frac{4}{8} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{27}{8}-\frac{-5-4}{8}\left(-\frac{9}{4}\right)$$

Subtract 4 from -5 to get -9.

$$-\frac{27}{8}-\left(-\frac{9}{8}\left(-\frac{9}{4}\right)\right)$$

Multiply -\frac{9}{8} times -\frac{9}{4} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{27}{8}-\frac{-9\left(-9\right)}{8\times 4}$$

Do the multiplications in the fraction \frac{-9\left(-9\right)}{8\times 4}.

$$-\frac{27}{8}-\frac{81}{32}$$

Least common multiple of 8 and 32 is 32. Convert -\frac{27}{8} and \frac{81}{32} to fractions with denominator 32.

$$-\frac{108}{32}-\frac{81}{32}$$

Since -\frac{108}{32} and \frac{81}{32} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-108-81}{32}$$

Subtract 81 from -108 to get -189.

$$-\frac{189}{32}$$

Factor

$$-\frac{189}{32} = -5\frac{29}{32} = -5.90625$$