Solve (5*x*y)^{3}=5^{3}*x^3*y^3=125*x^3*y^3

$$( 5 \cdot x \cdot y ) ^ { 3 } = 5 ^ { 3 } \cdot x ^ { 3 } \cdot y ^ { 3 } = 125 \cdot x ^ { 3 } \cdot y ^ { 3 }$$

Evaluate (complex solution)

Solution Steps

Expand \left(5xy\right)^{3}.

$$5^{3}x^{3}y^{3}=5^{3}x^{3}y^{3}\text{ and }5^{3}x^{3}y^{3}=125x^{3}y^{3}$$

Calculate 5 to the power of 3 and get 125.

$$125x^{3}y^{3}=5^{3}x^{3}y^{3}\text{ and }5^{3}x^{3}y^{3}=125x^{3}y^{3}$$

Calculate 5 to the power of 3 and get 125.

$$125x^{3}y^{3}=125x^{3}y^{3}\text{ and }5^{3}x^{3}y^{3}=125x^{3}y^{3}$$

Calculate 5 to the power of 3 and get 125.

$$125x^{3}y^{3}=125x^{3}y^{3}\text{ and }125x^{3}y^{3}=125x^{3}y^{3}$$

Subtract 125x^{3}y^{3} from both sides.

$$125x^{3}y^{3}-125x^{3}y^{3}=0\text{ and }125x^{3}y^{3}=125x^{3}y^{3}$$

Combine 125x^{3}y^{3} and -125x^{3}y^{3} to get 0.

$$0=0\text{ and }125x^{3}y^{3}=125x^{3}y^{3}$$

Compare 0 and 0.

$$\text{true}\text{ and }125x^{3}y^{3}=125x^{3}y^{3}$$

Subtract 125x^{3}y^{3} from both sides.

$$\text{true}\text{ and }125x^{3}y^{3}-125x^{3}y^{3}=0$$

Combine 125x^{3}y^{3} and -125x^{3}y^{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

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

Solve for y

$$y\in \mathrm{R}$$