Solve 500mm*500mm=x

$$500 mm \cdot 500 mm = x$$

Solve for x

$$x=250000m^{4}$$

Solution Steps

Multiply m and m to get m^{2}.

$$500m^{2}\times 500mm=x$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$500m^{3}\times 500m=x$$

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

$$500m^{4}\times 500=x$$

Multiply 500 and 500 to get 250000.

$$250000m^{4}=x$$

Swap sides so that all variable terms are on the left hand side.

$$x=250000m^{4}$$

Solve for m (complex solution)

$$m=\frac{\sqrt{5}\sqrt[4]{x}}{50}$$

$$m=-\frac{\sqrt{5}\sqrt[4]{x}}{50}$$

$$m=-\frac{\sqrt{5}i\sqrt[4]{x}}{50}$$

$$m=\frac{\sqrt{5}i\sqrt[4]{x}}{50}$$

Solve for m

$$\left\{\begin{matrix}m=-\frac{\sqrt{5}\sqrt[4]{x}}{50}\text{; }m=\frac{\sqrt{5}\sqrt[4]{x}}{50}\text{, }&x\geq 0\\m=0\text{, }&x=0\end{matrix}\right.$$