Solve x^2/x^5=x^-3

$$\frac { x ^ { 2 } } { x ^ { 5 } } = x ^ { - 3 }$$

Solve for x

$$x\neq 0$$

Solution Steps

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x^{5}.

$$x^{2}=x^{5}x^{-3}$$

To multiply powers of the same base, add their exponents. Add 5 and -3 to get 2.

$$x^{2}=x^{2}$$

Subtract x^{2} from both sides.

$$x^{2}-x^{2}=0$$

Combine x^{2} and -x^{2} to get 0.

$$0=0$$

Compare 0 and 0.

$$\text{true}$$

This is true for any x.

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

Variable x cannot be equal to 0.

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