Solve x(x^2)(x^4)=x^7

$$x ( x ^ { 2 } ) ( x ^ { 4 } ) = x ^ { 7 }$$

Solve for x (complex solution)

$$x\in \mathrm{C}$$

Solution Steps

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

$$x^{3}x^{4}=x^{7}$$

To multiply powers of the same base, add their exponents. Add 3 and 4 to get 7.

$$x^{7}=x^{7}$$

Subtract x^{7} from both sides.

$$x^{7}-x^{7}=0$$

Combine x^{7} and -x^{7} to get 0.

$$0=0$$

Compare 0 and 0.

$$\text{true}$$

This is true for any x.

$$x\in \mathrm{C}$$

Solve for x

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

Solution Steps

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

$$x^{3}x^{4}=x^{7}$$

To multiply powers of the same base, add their exponents. Add 3 and 4 to get 7.

$$x^{7}=x^{7}$$

Subtract x^{7} from both sides.

$$x^{7}-x^{7}=0$$

Combine x^{7} and -x^{7} to get 0.

$$0=0$$

Compare 0 and 0.

$$\text{true}$$

This is true for any x.

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