1. **State the problem:** Solve for $m$ in the equation $2^m = 64$. 2. **Recall the formula and rules:** The equation $a^x = b$ can be solved by expressing $b$ as a power of $a$ if possible, then equating the exponents. 3. **Express 64 as a power of 2:** Since $64 = 2^6$, rewrite the equation as: $$2^m = 2^6$$ 4. **Equate the exponents:** Because the bases are the same and nonzero, the exponents must be equal: $$m = 6$$ 5. **Final answer:** $m = 6$