Solve for \( x \) \( (4 x-3)^{3 / 5}=8 \) \( x=\square \) \( \rightarrow \) Next Question

1. Start with the equation: \[ (4x - 3)^{\frac{3}{5}} = 8 \] 2. To eliminate the fractional exponent, raise both sides to the power of \(\frac{5}{3}\): \[ \left((4x - 3)^{\frac{3}{5}}\right)^{\frac{5}{3}} = 8^{\frac{5}{3}} \] 3. Simplify the left side using the property \(\left(a^b\right)^c = a^{bc}\): \[ 4x - 3 = 8^{\frac{5}{3}} \] 4. Rewrite \(8\) as \(2^3\) and simplify the right side: \[ 8^{\frac{5}{3}} = (2^3)^{\frac{5}{3}} = 2^{3 \cdot \frac{5}{3}} = 2^5 = 32 \] 5. The equation now becomes: \[ 4x - 3 = 32 \] 6. Solve for \(x\) by adding 3 to both sides: \[ 4x = 32 + 3 = 35 \] 7. Divide both sides by 4: \[ x = \frac{35}{4} \] \( x = \frac{35}{4} \)