Solve (x/2)^3=x^3/8

$$( \frac { x } { 2 } ) ^ { 3 } = \frac { x ^ { 3 } } { 8 }$$

Solve for x (complex solution)

$$x\in \mathrm{C}$$

Solution Steps

Multiply both sides of the equation by 8.

$$8\times \left(\frac{x}{2}\right)^{3}=x^{3}$$

To raise \frac{x}{2} to a power, raise both numerator and denominator to the power and then divide.

$$8\times \frac{x^{3}}{2^{3}}=x^{3}$$

Express 8\times \frac{x^{3}}{2^{3}} as a single fraction.

$$\frac{8x^{3}}{2^{3}}=x^{3}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{8x^{3}}{8}=x^{3}$$

Cancel out 8 and 8.

$$x^{3}=x^{3}$$

Subtract x^{3} from both sides.

$$x^{3}-x^{3}=0$$

Combine x^{3} and -x^{3} to get 0.

$$0=0$$

Compare 0 and 0.

$$\text{true}$$

This is true for any x.

$$x\in \mathrm{C}$$

Solve for x

$$x\in \mathrm{R}$$

Solution Steps

Multiply both sides of the equation by 8.

$$8\times \left(\frac{x}{2}\right)^{3}=x^{3}$$

To raise \frac{x}{2} to a power, raise both numerator and denominator to the power and then divide.

$$8\times \frac{x^{3}}{2^{3}}=x^{3}$$

Express 8\times \frac{x^{3}}{2^{3}} as a single fraction.

$$\frac{8x^{3}}{2^{3}}=x^{3}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{8x^{3}}{8}=x^{3}$$

Cancel out 8 and 8.

$$x^{3}=x^{3}$$

Subtract x^{3} from both sides.

$$x^{3}-x^{3}=0$$

Combine x^{3} and -x^{3} to get 0.

$$0=0$$

Compare 0 and 0.

$$\text{true}$$

This is true for any x.

$$x\in \mathrm{R}$$