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

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

Evaluate (complex solution)

Solution Steps

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

$$x^{2}=x^{2}\text{ and }x^{2}=x^{-3+5}$$

Add -3 and 5 to get 2.

$$x^{2}=x^{2}\text{ and }x^{2}=x^{2}$$

Subtract x^{2} from both sides.

$$x^{2}-x^{2}=0\text{ and }x^{2}=x^{2}$$

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

$$0=0\text{ and }x^{2}=x^{2}$$

Compare 0 and 0.

$$\text{true}\text{ and }x^{2}=x^{2}$$

Subtract x^{2} from both sides.

$$\text{true}\text{ and }x^{2}-x^{2}=0$$

Combine x^{2} and -x^{2} 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

$$x\neq 0$$