Solve xxxxxxx=y

$$xxxxxxx=y$$

Solve for y

$$y=x^{7}$$

Solution Steps

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

$$x^{2}xxxxx=y$$

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

$$x^{3}xxxx=y$$

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

$$x^{4}xxx=y$$

To multiply powers of the same base, add their exponents. Add 4 and 1 to get 5.

$$x^{5}xx=y$$

To multiply powers of the same base, add their exponents. Add 5 and 1 to get 6.

$$x^{6}x=y$$

To multiply powers of the same base, add their exponents. Add 6 and 1 to get 7.

$$x^{7}=y$$

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

$$y=x^{7}$$

Solve for x (complex solution)

$$x\in e^{\frac{2\pi i}{7}}\sqrt[7]{y},\sqrt[7]{y},e^{\frac{4\pi i}{7}}\sqrt[7]{y},e^{\frac{6\pi i}{7}}\sqrt[7]{y},e^{\frac{8\pi i}{7}}\sqrt[7]{y},e^{\frac{10\pi i}{7}}\sqrt[7]{y},e^{\frac{12\pi i}{7}}\sqrt[7]{y}$$

Solve for x

$$x=\sqrt[7]{y}$$