7. Solve for \( x \) : a) \( x^{\frac{2}{3}}=16 \)

To solve \( x^{\frac{2}{3}} = 16 \), start by raising both sides to the power of \( \frac{3}{2} \). This cancels out the exponent on the left side: \[ x = 16^{\frac{3}{2}}. \] Now, calculate \( 16^{\frac{3}{2}} \): First, find \( 16^{\frac{1}{2}} = 4 \); then, raise it to the power of 3: \[ 4^3 = 64. \] Therefore, \( x = 64 \). So, the solution is \( x = 64 \).