Solve -2^3-2/3^2/frac{1{3}+22^2(3)}

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

Evaluate

$$-\frac{74}{219}\approx -0.337899543$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$\frac{-2^{3}-\frac{2}{3^{2}}}{\frac{1}{3}+2^{3}\times 3}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{-8-\frac{2}{3^{2}}}{\frac{1}{3}+2^{3}\times 3}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{-8-\frac{2}{9}}{\frac{1}{3}+2^{3}\times 3}$$

Convert -8 to fraction -\frac{72}{9}.

$$\frac{-\frac{72}{9}-\frac{2}{9}}{\frac{1}{3}+2^{3}\times 3}$$

Since -\frac{72}{9} and \frac{2}{9} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{-72-2}{9}}{\frac{1}{3}+2^{3}\times 3}$$

Subtract 2 from -72 to get -74.

$$\frac{-\frac{74}{9}}{\frac{1}{3}+2^{3}\times 3}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{-\frac{74}{9}}{\frac{1}{3}+8\times 3}$$

Multiply 8 and 3 to get 24.

$$\frac{-\frac{74}{9}}{\frac{1}{3}+24}$$

Convert 24 to fraction \frac{72}{3}.

$$\frac{-\frac{74}{9}}{\frac{1}{3}+\frac{72}{3}}$$

Since \frac{1}{3} and \frac{72}{3} have the same denominator, add them by adding their numerators.

$$\frac{-\frac{74}{9}}{\frac{1+72}{3}}$$

Add 1 and 72 to get 73.

$$\frac{-\frac{74}{9}}{\frac{73}{3}}$$

Divide -\frac{74}{9} by \frac{73}{3} by multiplying -\frac{74}{9} by the reciprocal of \frac{73}{3}.

$$-\frac{74}{9}\times \frac{3}{73}$$

Multiply -\frac{74}{9} times \frac{3}{73} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-74\times 3}{9\times 73}$$

Do the multiplications in the fraction \frac{-74\times 3}{9\times 73}.

$$\frac{-222}{657}$$

Reduce the fraction \frac{-222}{657} to lowest terms by extracting and canceling out 3.

$$-\frac{74}{219}$$

Factor

$$-\frac{74}{219} = -0.3378995433789954$$