Solve 677=x1sqrt[3]{5sqrt{34x/263}}

$$677=x1 \sqrt[3]{ 5 \sqrt{ 34 \frac{ x }{ 263 } } }$$

Solve for x_1

$$x_{1}=\frac{677\times 5^{\frac{2}{3}}\times 34^{\frac{5}{6}}\sqrt[6]{\frac{263}{x}}}{170}$$

$$x>0$$

Steps for Solving Linear Equation

Express 34\times \frac{x}{263} as a single fraction.

$$677=x_{1}\sqrt[3]{5\sqrt{\frac{34x}{263}}}$$

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

$$x_{1}\sqrt[3]{5\sqrt{\frac{34x}{263}}}=677$$

The equation is in standard form.

$$\sqrt[3]{5\sqrt{\frac{34x}{263}}}x_{1}=677$$

Divide both sides by \sqrt[3]{5\sqrt{\frac{34}{263}x}}.

$$\frac{\sqrt[3]{5\sqrt{\frac{34x}{263}}}x_{1}}{\sqrt[3]{5\sqrt{\frac{34x}{263}}}}=\frac{677}{\sqrt[3]{5\sqrt{\frac{34x}{263}}}}$$

Dividing by \sqrt[3]{5\sqrt{\frac{34}{263}x}} undoes the multiplication by \sqrt[3]{5\sqrt{\frac{34}{263}x}}.

$$x_{1}=\frac{677}{\sqrt[3]{5\sqrt{\frac{34x}{263}}}}$$

Divide 677 by \sqrt[3]{5\sqrt{\frac{34}{263}x}}.

$$x_{1}=\frac{677\sqrt[6]{263}}{\sqrt[3]{5}\sqrt[6]{34x}}$$

Solve for x

$$x=\frac{25321402728434011007}{850x_{1}^{6}}$$

$$x_{1}>0$$