Question Find the positive solution of the equation. \[ 8 x^{\frac{7}{4}}+16=38263768 \]

Solve the equation \( 8x^{\frac{7}{4}}+16=38263768 \). Solve the equation by following steps: - step0: Solve for \(x\): \(8x^{\frac{7}{4}}+16=38263768\) - step1: Find the domain: \(8x^{\frac{7}{4}}+16=38263768,x\geq 0\) - step2: Move the constant to the right side: \(8x^{\frac{7}{4}}=38263768-16\) - step3: Subtract the numbers: \(8x^{\frac{7}{4}}=38263752\) - step4: Divide both sides: \(\frac{8x^{\frac{7}{4}}}{8}=\frac{38263752}{8}\) - step5: Divide the numbers: \(x^{\frac{7}{4}}=4782969\) - step6: Raise both sides to the \(\frac{4}{7}\)-th power\(:\) \(\left(x^{\frac{7}{4}}\right)^{\frac{4}{7}}=4782969^{\frac{4}{7}}\) - step7: Evaluate the power: \(x=6561\) - step8: Check if the solution is in the defined range: \(x=6561,x\geq 0\) - step9: Find the intersection: \(x=6561\) The positive solution of the equation \(8x^{\frac{7}{4}}+16=38263768\) is \(x=6561\).