Question: Solve: $a^{3/4} = 125$
1. **State the problem:** We need to solve the equation $$a^{3/4} = 125$$ for $a$.
2. **Recall the formula and rules:** To solve for $a$, we want to isolate it by raising both sides of the equation to the reciprocal power of $3/4$, which is $4/3$.
3. **Apply the reciprocal power:**
$$\left(a^{3/4}\right)^{4/3} = 125^{4/3}$$
4. **Simplify the left side using the power of a power rule:**
$$a^{(3/4) \times (4/3)} = a^1 = a$$
5. **Calculate the right side:**
First, express $125$ as a power of $5$:
$$125 = 5^3$$
So,
$$125^{4/3} = (5^3)^{4/3} = 5^{3 \times \frac{4}{3}} = 5^4 = 625$$
6. **Final answer:**
$$a = 625$$