Find the positive solution of the equation. 7x^(6)/(7)+30=109405 Answer Attemptiout of 2 square

To find the positive solution of the equation \(7x^{\frac{6}{7}} + 30 = 109405\), follow these steps:<br /><br />1. **Isolate the term with the variable:**<br /> \[<br /> 7x^{\frac{6}{7}} + 30 = 109405<br /> \]<br /> Subtract 30 from both sides:<br /> \[<br /> 7x^{\frac{6}{7}} = 109375<br /> \]<br /><br />2. **Solve for \(x^{\frac{6}{7}}\):**<br /> Divide both sides by 7:<br /> \[<br /> x^{\frac{6}{7}} = \frac{109375}{7}<br /> \]<br /> Simplify the fraction:<br /> \[<br /> x^{\frac{6}{7}} = 15625<br /> \]<br /><br />3. **Solve for \(x\):**<br /> Raise both sides to the power of \(\frac{7}{6}\) to isolate \(x\):<br /> \[<br /> x = (15625)^{\frac{7}{6}}<br /> \]<br /><br />4. **Simplify the expression:**<br /> Recognize that \(15625 = 5^6\):<br /> \[<br /> x = (5^6)^{\frac{7}{6}}<br /> \]<br /> Apply the exponent rule \((a^m)^n = a^{mn}\):<br /> \[<br /> x = 5^7<br /> \]<br /><br />5. **Calculate the final value:**<br /> \[<br /> 5^7 = 78125<br /> \]<br /><br />Therefore, the positive solution of the equation is:<br />\[<br />\boxed{78125}<br />\]