\( (625)^{\frac{1}{4}}= \) (A) \( \frac{1}{625} \) B 5 (C) \( \frac{1}{5} \) (D) 20

To solve \( (625)^{\frac{1}{4}} \), we can first rewrite 625 as \( 5^4 \) because \( 5 \times 5 \times 5 \times 5 = 625 \). So, \( (625)^{\frac{1}{4}} = (5^4)^{\frac{1}{4}} = 5^{(4 \cdot \frac{1}{4})} = 5^1 = 5 \). Therefore, the correct answer is B) 5. Now, if you're wondering about the significance of this calculation, roots and exponents are foundational in mathematics. This particular type—finding the fourth root—is used in various fields, including engineering and physics, where scaling down quantities is necessary. For anyone attempting similar problems, remember that breaking down numbers into their prime factors can simplify your calculations dramatically. One common mistake is forgetting the properties of exponents, like the rule \( (a^m)^n = a^{m \cdot n} \), which can lead to confusion when dealing with roots and powers.