Solve (2m^3)^2div(2m)^2=m^4

$$( 2 m ^ { 3 } ) ^ { 2 } \div ( 2 m ) ^ { 2 } = m ^ { 4 }$$

Solve for m

$$m\neq 0$$

Solution Steps

Variable m cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 4m^{2}.

$$\left(2m^{3}\right)^{2}=4m^{2}m^{4}$$

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

$$2^{2}\left(m^{3}\right)^{2}=4m^{2}m^{4}$$

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

$$2^{2}m^{6}=4m^{2}m^{4}$$

Calculate 2 to the power of 2 and get 4.

$$4m^{6}=4m^{2}m^{4}$$

To multiply powers of the same base, add their exponents. Add 2 and 4 to get 6.

$$4m^{6}=4m^{6}$$

Subtract 4m^{6} from both sides.

$$4m^{6}-4m^{6}=0$$

Combine 4m^{6} and -4m^{6} to get 0.

$$0=0$$

Compare 0 and 0.

$$\text{true}$$

This is true for any m.

$$m\in \mathrm{R}$$

Variable m cannot be equal to 0.

$$m\in \mathrm{R}\setminus 0$$