c. \( \sqrt{2^{x+1}}=8^{\prime} \)

To solve the equation \( \sqrt{2^{x+1}}=8 \), remember that \( \sqrt{a} = a^{1/2} \). This means we can rewrite the left side as \( (2^{x+1})^{1/2} = 2^{(x+1)/2} \). Now, since \( 8 \) can be expressed as \( 2^3 \), we can equate the exponents: \[ 2^{(x+1)/2} = 2^3. \] This leads us to: \[ \frac{x+1}{2} = 3. \] Multiplying both sides by \( 2 \) gives \( x + 1 = 6 \). Finally, subtract \( 1 \) from both sides to find \( x = 5 \). Get ready to celebrate your solution! 🎉 If you can manipulate exponents and square roots, you're on your way to becoming a math wizard!