Solve -2^4/{left(frac{8{3}right)}^2}+51/2*(-1/6)--0.5^2

$$\frac{ - { 2 }^{ 4 } }{ { \left( \frac{ 8 }{ 3 } \right) }^{ 2 } } +5 \frac{ 1 }{ 2 } \times (- \frac{ 1 }{ 6 } )- { -0.5 }^{ 2 }$$

Evaluate

$$-\frac{41}{12}\approx -3.416666667$$

Solution Steps

Calculate 2 to the power of 4 and get 16.

$$\frac{-16}{\left(\frac{8}{3}\right)^{2}}+\frac{5\times 2+1}{2}\left(-\frac{1}{6}\right)-\left(-0.5\right)^{2}$$

Calculate \frac{8}{3} to the power of 2 and get \frac{64}{9}.

$$\frac{-16}{\frac{64}{9}}+\frac{5\times 2+1}{2}\left(-\frac{1}{6}\right)-\left(-0.5\right)^{2}$$

Divide -16 by \frac{64}{9} by multiplying -16 by the reciprocal of \frac{64}{9}.

$$-16\times \frac{9}{64}+\frac{5\times 2+1}{2}\left(-\frac{1}{6}\right)-\left(-0.5\right)^{2}$$

Express -16\times \frac{9}{64} as a single fraction.

$$\frac{-16\times 9}{64}+\frac{5\times 2+1}{2}\left(-\frac{1}{6}\right)-\left(-0.5\right)^{2}$$

Multiply -16 and 9 to get -144.

$$\frac{-144}{64}+\frac{5\times 2+1}{2}\left(-\frac{1}{6}\right)-\left(-0.5\right)^{2}$$

Reduce the fraction \frac{-144}{64} to lowest terms by extracting and canceling out 16.

$$-\frac{9}{4}+\frac{5\times 2+1}{2}\left(-\frac{1}{6}\right)-\left(-0.5\right)^{2}$$

Multiply 5 and 2 to get 10.

$$-\frac{9}{4}+\frac{10+1}{2}\left(-\frac{1}{6}\right)-\left(-0.5\right)^{2}$$

Add 10 and 1 to get 11.

$$-\frac{9}{4}+\frac{11}{2}\left(-\frac{1}{6}\right)-\left(-0.5\right)^{2}$$

Multiply \frac{11}{2} times -\frac{1}{6} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{9}{4}+\frac{11\left(-1\right)}{2\times 6}-\left(-0.5\right)^{2}$$

Do the multiplications in the fraction \frac{11\left(-1\right)}{2\times 6}.

$$-\frac{9}{4}+\frac{-11}{12}-\left(-0.5\right)^{2}$$

Fraction \frac{-11}{12} can be rewritten as -\frac{11}{12} by extracting the negative sign.

$$-\frac{9}{4}-\frac{11}{12}-\left(-0.5\right)^{2}$$

Least common multiple of 4 and 12 is 12. Convert -\frac{9}{4} and \frac{11}{12} to fractions with denominator 12.

$$-\frac{27}{12}-\frac{11}{12}-\left(-0.5\right)^{2}$$

Since -\frac{27}{12} and \frac{11}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-27-11}{12}-\left(-0.5\right)^{2}$$

Subtract 11 from -27 to get -38.

$$\frac{-38}{12}-\left(-0.5\right)^{2}$$

Reduce the fraction \frac{-38}{12} to lowest terms by extracting and canceling out 2.

$$-\frac{19}{6}-\left(-0.5\right)^{2}$$

Calculate -0.5 to the power of 2 and get 0.25.

$$-\frac{19}{6}-0.25$$

Convert decimal number 0.25 to fraction \frac{25}{100}. Reduce the fraction \frac{25}{100} to lowest terms by extracting and canceling out 25.

$$-\frac{19}{6}-\frac{1}{4}$$

Least common multiple of 6 and 4 is 12. Convert -\frac{19}{6} and \frac{1}{4} to fractions with denominator 12.

$$-\frac{38}{12}-\frac{3}{12}$$

Since -\frac{38}{12} and \frac{3}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-38-3}{12}$$

Subtract 3 from -38 to get -41.

$$-\frac{41}{12}$$

Factor

$$-\frac{41}{12} = -3\frac{5}{12} = -3.4166666666666665$$