Solve (64*3^3/-81)/{left(frac{12*3^5{9}right)}^2}

$$\frac{ ( \frac{ 64 \times { 3 }^{ 3 } }{ -81 } ) }{ { \left( \frac{ 12 \times { 3 }^{ 5 } }{ 9 } \right) }^{ 2 } }$$

Evaluate

$$-\frac{4}{19683}\approx -0.000203221$$

Solution Steps

Calculate 3 to the power of 3 and get 27.

$$\frac{\frac{64\times 27}{-81}}{\left(\frac{12\times 3^{5}}{9}\right)^{2}}$$

Multiply 64 and 27 to get 1728.

$$\frac{\frac{1728}{-81}}{\left(\frac{12\times 3^{5}}{9}\right)^{2}}$$

Reduce the fraction \frac{1728}{-81} to lowest terms by extracting and canceling out 27.

$$\frac{-\frac{64}{3}}{\left(\frac{12\times 3^{5}}{9}\right)^{2}}$$

Calculate 3 to the power of 5 and get 243.

$$\frac{-\frac{64}{3}}{\left(\frac{12\times 243}{9}\right)^{2}}$$

Multiply 12 and 243 to get 2916.

$$\frac{-\frac{64}{3}}{\left(\frac{2916}{9}\right)^{2}}$$

Divide 2916 by 9 to get 324.

$$\frac{-\frac{64}{3}}{324^{2}}$$

Calculate 324 to the power of 2 and get 104976.

$$\frac{-\frac{64}{3}}{104976}$$

Express \frac{-\frac{64}{3}}{104976} as a single fraction.

$$\frac{-64}{3\times 104976}$$

Multiply 3 and 104976 to get 314928.

$$\frac{-64}{314928}$$

Reduce the fraction \frac{-64}{314928} to lowest terms by extracting and canceling out 16.

$$-\frac{4}{19683}$$

Factor

$$-\frac{4}{19683} = -0.00020322105370116343$$