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

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

Evaluate

$$-\frac{16384}{177147}\approx -0.09248816$$

Solution Steps

Calculate 3 to the power of 3 and get 27.

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

Multiply 64 and 27 to get 1728.

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

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

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

Calculate -\frac{64}{3} to the power of 3 and get -\frac{262144}{27}.

$$\frac{-\frac{262144}{27}}{\left(\frac{12\times 3^{5}}{9}\right)^{2}}$$

Calculate 3 to the power of 5 and get 243.

$$\frac{-\frac{262144}{27}}{\left(\frac{12\times 243}{9}\right)^{2}}$$

Multiply 12 and 243 to get 2916.

$$\frac{-\frac{262144}{27}}{\left(\frac{2916}{9}\right)^{2}}$$

Divide 2916 by 9 to get 324.

$$\frac{-\frac{262144}{27}}{324^{2}}$$

Calculate 324 to the power of 2 and get 104976.

$$\frac{-\frac{262144}{27}}{104976}$$

Express \frac{-\frac{262144}{27}}{104976} as a single fraction.

$$\frac{-262144}{27\times 104976}$$

Multiply 27 and 104976 to get 2834352.

$$\frac{-262144}{2834352}$$

Reduce the fraction \frac{-262144}{2834352} to lowest terms by extracting and canceling out 16.

$$-\frac{16384}{177147}$$

Factor

$$-\frac{16384}{177147} = -0.09248815955110727$$