1. Write the balanced chemical equation:

HClO₄ (aq) + NaOH (aq) → NaClO₄ (aq) + H₂O (l)

2. Determine the moles of NaOH:

* Moles = Molarity * Volume (in liters)

* Moles of NaOH = (8.65 x 10⁻² M) * (60 mL / 1000 mL/L) = 5.19 x 10⁻³ mol

3. Use stoichiometry to find moles of HClO₄:

* From the balanced equation, 1 mole of HClO₄ reacts with 1 mole of NaOH.

* Therefore, moles of HClO₄ needed = 5.19 x 10⁻³ mol

4. Calculate the volume of HClO₄ solution:

* Volume = Moles / Molarity

* Volume of HClO₄ = (5.19 x 10⁻³ mol) / (0.150 M) = 0.0346 L

5. Convert to milliliters:

* Volume of HClO₄ = 0.0346 L * 1000 mL/L = 34.6 mL

Answer: You need 34.6 mL of 0.150 M HClO₄ solution to neutralize 60 mL of 8.65 x 10⁻² M NaOH solution.