Solve (2xp/6x^{2})^3=(p/3x)^3=p^3/27x^3

$$( \frac { 2 x p } { 6 x ^ { 2 } } ) ^ { 3 } = ( \frac { p } { 3 x } ) ^ { 3 } = \frac { p ^ { 3 } } { 27 x ^ { 3 } }$$

Evaluate (complex solution)

Solution Steps

Cancel out 2x in both numerator and denominator.

$$\left(\frac{p}{3x}\right)^{3}=\left(\frac{p}{3x}\right)^{3}\text{ and }\left(\frac{p}{3x}\right)^{3}=\frac{p^{3}}{27x^{3}}$$

To raise \frac{p}{3x} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{p^{3}}{\left(3x\right)^{3}}=\left(\frac{p}{3x}\right)^{3}\text{ and }\left(\frac{p}{3x}\right)^{3}=\frac{p^{3}}{27x^{3}}$$

To raise \frac{p}{3x} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{p^{3}}{\left(3x\right)^{3}}=\frac{p^{3}}{\left(3x\right)^{3}}\text{ and }\left(\frac{p}{3x}\right)^{3}=\frac{p^{3}}{27x^{3}}$$

To raise \frac{p}{3x} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{p^{3}}{\left(3x\right)^{3}}=\frac{p^{3}}{\left(3x\right)^{3}}\text{ and }\frac{p^{3}}{\left(3x\right)^{3}}=\frac{p^{3}}{27x^{3}}$$

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

$$\frac{p^{3}}{3^{3}x^{3}}=\frac{p^{3}}{\left(3x\right)^{3}}\text{ and }\frac{p^{3}}{\left(3x\right)^{3}}=\frac{p^{3}}{27x^{3}}$$

Calculate 3 to the power of 3 and get 27.

$$\frac{p^{3}}{27x^{3}}=\frac{p^{3}}{\left(3x\right)^{3}}\text{ and }\frac{p^{3}}{\left(3x\right)^{3}}=\frac{p^{3}}{27x^{3}}$$

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

$$\frac{p^{3}}{27x^{3}}=\frac{p^{3}}{3^{3}x^{3}}\text{ and }\frac{p^{3}}{\left(3x\right)^{3}}=\frac{p^{3}}{27x^{3}}$$

Calculate 3 to the power of 3 and get 27.

$$\frac{p^{3}}{27x^{3}}=\frac{p^{3}}{27x^{3}}\text{ and }\frac{p^{3}}{\left(3x\right)^{3}}=\frac{p^{3}}{27x^{3}}$$

Subtract \frac{p^{3}}{27x^{3}} from both sides.

$$\frac{p^{3}}{27x^{3}}-\frac{p^{3}}{27x^{3}}=0\text{ and }\frac{p^{3}}{\left(3x\right)^{3}}=\frac{p^{3}}{27x^{3}}$$

Subtract \frac{p^{3}}{27x^{3}} from \frac{p^{3}}{27x^{3}} to get 0.

$$0=0\text{ and }\frac{p^{3}}{\left(3x\right)^{3}}=\frac{p^{3}}{27x^{3}}$$

Compare 0 and 0.

$$\text{true}\text{ and }\frac{p^{3}}{\left(3x\right)^{3}}=\frac{p^{3}}{27x^{3}}$$

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

$$\text{true}\text{ and }\frac{p^{3}}{3^{3}x^{3}}=\frac{p^{3}}{27x^{3}}$$

Calculate 3 to the power of 3 and get 27.

$$\text{true}\text{ and }\frac{p^{3}}{27x^{3}}=\frac{p^{3}}{27x^{3}}$$

Subtract \frac{p^{3}}{27x^{3}} from both sides.

$$\text{true}\text{ and }\frac{p^{3}}{27x^{3}}-\frac{p^{3}}{27x^{3}}=0$$

Subtract \frac{p^{3}}{27x^{3}} from \frac{p^{3}}{27x^{3}} to get 0.

$$\text{true}\text{ and }0=0$$

Compare 0 and 0.

$$\text{true}\text{ and }\text{true}$$

The conjunction of \text{true} and \text{true} is \text{true}.

$$\text{true}$$

Solve for x

$$x\neq 0$$

Solve for p

$$p\in \mathrm{R}$$

$$x\neq 0$$