Solve frac{(3x)^{2}}{3(mn)^0}*(-3n)^3/2(x^3)^2

$$\frac { ( 3 x ) ^ { 2 } } { 3 ( m n ) ^ { 0 } } \times \frac { ( - 3 n ) ^ { 3 } } { 2 ( x ^ { 3 } ) ^ { 2 } }$$

Evaluate

$$-\frac{81n^{3}}{2x^{4}}$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$\frac{\left(3x\right)^{2}}{3\left(mn\right)^{0}}\times \frac{\left(-3n\right)^{3}}{2x^{6}}$$

Expand \left(3x\right)^{2}.

$$\frac{3^{2}x^{2}}{3\left(mn\right)^{0}}\times \frac{\left(-3n\right)^{3}}{2x^{6}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{9x^{2}}{3\left(mn\right)^{0}}\times \frac{\left(-3n\right)^{3}}{2x^{6}}$$

Calculate mn to the power of 0 and get 1.

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

Multiply 3 and 1 to get 3.

$$\frac{9x^{2}}{3}\times \frac{\left(-3n\right)^{3}}{2x^{6}}$$

Divide 9x^{2} by 3 to get 3x^{2}.

$$3x^{2}\times \frac{\left(-3n\right)^{3}}{2x^{6}}$$

Expand \left(-3n\right)^{3}.

$$3x^{2}\times \frac{\left(-3\right)^{3}n^{3}}{2x^{6}}$$

Calculate -3 to the power of 3 and get -27.

$$3x^{2}\times \frac{-27n^{3}}{2x^{6}}$$

Express 3\times \frac{-27n^{3}}{2x^{6}} as a single fraction.

$$\frac{3\left(-27\right)n^{3}}{2x^{6}}x^{2}$$

Multiply 3 and -27 to get -81.

$$\frac{-81n^{3}}{2x^{6}}x^{2}$$

Express \frac{-81n^{3}}{2x^{6}}x^{2} as a single fraction.

$$\frac{-81n^{3}x^{2}}{2x^{6}}$$

Cancel out x^{2} in both numerator and denominator.

$$\frac{-81n^{3}}{2x^{4}}$$

Differentiate w.r.t. x

$$\frac{162n^{3}}{x^{5}}$$