Find the positive solution of the equation. 3x^(3)/(7)-2=190 Answer Attemptiout of 2 square

To find the positive solution of the equation \(3x^{\frac{3}{7}} - 2 = 190\), follow these steps:<br /><br />1. **Isolate the term with the variable:**<br /> \[<br /> 3x^{\frac{3}{7}} - 2 = 190<br /> \]<br /> Add 2 to both sides:<br /> \[<br /> 3x^{\frac{3}{7}} = 192<br /> \]<br /><br />2. **Solve for \(x^{\frac{3}{7}}\):**<br /> Divide both sides by 3:<br /> \[<br /> x^{\frac{3}{7}} = \frac{192}{3}<br /> \]<br /> Simplify the right-hand side:<br /> \[<br /> x^{\frac{3}{7}} = 64<br /> \]<br /><br />3. **Solve for \(x\):**<br /> Raise both sides to the power of \(\frac{7}{3}\) to isolate \(x\):<br /> \[<br /> \left(x^{\frac{3}{7}}\right)^{\frac{7}{3}} = 64^{\frac{7}{3}}<br /> \]<br /> Simplify the left-hand side:<br /> \[<br /> x = 64^{\frac{7}{3}}<br /> \]<br /><br />4. **Simplify \(64^{\frac{7}{3}}\):**<br /> Recognize that \(64\) is \(4^3\):<br /> \[<br /> 64 = 4^3<br /> \]<br /> Substitute \(4^3\) into the expression:<br /> \[<br /> x = (4^3)^{\frac{7}{3}}<br /> \]<br /> Simplify the exponent:<br /> \[<br /> x = 4^{3 \cdot \frac{7}{3}}<br /> \]<br /> \[<br /> x = 4^7<br /> \]<br /><br />5. **Calculate \(4^7\):**<br /> \[<br /> 4^7 = 16384<br /> \]<br /><br />Therefore, the positive solution of the equation is:<br />\[<br />\boxed{16384}<br />\]