Solve -2^3/3+1/-2(-2^2)

$$\frac{ - { 2 }^{ 3 } }{ 3 } + \frac{ 1 }{ -2(- { 2 }^{ 2 } ) }$$

Evaluate

$$-\frac{61}{24}\approx -2.541666667$$

Solution Steps

Calculate 2 to the power of 3 and get 8.

$$\frac{-8}{3}+\frac{1}{-2\left(-2^{2}\right)}$$

Fraction \frac{-8}{3} can be rewritten as -\frac{8}{3} by extracting the negative sign.

$$-\frac{8}{3}+\frac{1}{-2\left(-2^{2}\right)}$$

Calculate 2 to the power of 2 and get 4.

$$-\frac{8}{3}+\frac{1}{-2\left(-4\right)}$$

Multiply -2 and -4 to get 8.

$$-\frac{8}{3}+\frac{1}{8}$$

Least common multiple of 3 and 8 is 24. Convert -\frac{8}{3} and \frac{1}{8} to fractions with denominator 24.

$$-\frac{64}{24}+\frac{3}{24}$$

Since -\frac{64}{24} and \frac{3}{24} have the same denominator, add them by adding their numerators.

$$\frac{-64+3}{24}$$

Add -64 and 3 to get -61.

$$-\frac{61}{24}$$

Factor

$$-\frac{61}{24} = -2\frac{13}{24} = -2.5416666666666665$$