Solve frac{2^{3}*3^{2}-3^6*2*1}{(-2)^1*3^3*(-2)^3}

$$\frac { 2 ^ { 3 } \cdot 3 ^ { 2 } - 3 ^ { 6 } \cdot 2 \cdot 1 } { ( - 2 ) ^ { 1 } \cdot 3 ^ { 3 } \cdot ( - 2 ) ^ { 3 } }$$

Evaluate

$$-\frac{77}{24}\approx -3.208333333$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.

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

Calculate 2 to the power of 3 and get 8.

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

Calculate 3 to the power of 2 and get 9.

$$\frac{8\times 9-3^{6}\times 2\times 1}{\left(-2\right)^{4}\times 3^{3}}$$

Multiply 8 and 9 to get 72.

$$\frac{72-3^{6}\times 2\times 1}{\left(-2\right)^{4}\times 3^{3}}$$

Calculate 3 to the power of 6 and get 729.

$$\frac{72-729\times 2\times 1}{\left(-2\right)^{4}\times 3^{3}}$$

Multiply 729 and 2 to get 1458.

$$\frac{72-1458\times 1}{\left(-2\right)^{4}\times 3^{3}}$$

Multiply 1458 and 1 to get 1458.

$$\frac{72-1458}{\left(-2\right)^{4}\times 3^{3}}$$

Subtract 1458 from 72 to get -1386.

$$\frac{-1386}{\left(-2\right)^{4}\times 3^{3}}$$

Calculate -2 to the power of 4 and get 16.

$$\frac{-1386}{16\times 3^{3}}$$

Calculate 3 to the power of 3 and get 27.

$$\frac{-1386}{16\times 27}$$

Multiply 16 and 27 to get 432.

$$\frac{-1386}{432}$$

Reduce the fraction \frac{-1386}{432} to lowest terms by extracting and canceling out 18.

$$-\frac{77}{24}$$

Factor

$$-\frac{77}{24} = -3\frac{5}{24} = -3.2083333333333335$$