Find the positive solution of the equation. 4x^(8)/(3)-1=23059203 Answer Attemptiout of 2 square

To find the positive solution of the equation \(4x^{\frac{8}{3}} - 1 = 23059203\), follow these steps:<br /><br />1. **Isolate the term with the variable:**<br /> \[<br /> 4x^{\frac{8}{3}} - 1 = 23059203<br /> \]<br /> Add both sides:<br /> \[<br /> 4x^{\frac{8}{3}} = 23059204<br /> \]<br /><br />2. **Solve for \(x^{\frac{8}{3}}\):**<br /> Divide both sides by 4:<br /> \[<br /> x^{\frac{8}{3}} = \frac{23059204}{4}<br /> \]<br /> Calculate the division:<br /> \[<br /> x^{\frac{8}{3}} = 5764801<br /> \]<br /><br />3. **Solve for \(x\):**<br /> Raise both sides to the power of \(\frac{3}{8}\) to isolate \(x\):<br /> \[<br /> x = \left(5764801\right)^{\frac{3}{8}}<br /> \]<br /><br />4. **Calculate the value:**<br /> \[<br /> x = \left(5764801\right)^{\frac{3}{8}}<br /> \]<br /> Using a calculator or computational tool:<br /> \[<br /> x = 256<br /> \]<br /><br />So, the positive solution of the equation is:<br />\[<br />\boxed{256}<br />\]