(d) \( \sqrt{\left(\frac{1}{4}\right)^{3}} \)

To simplify \( \sqrt{\left(\frac{1}{4}\right)^{3}} \), start by raising \(\frac{1}{4}\) to the power of 3. This gives you \(\left(\frac{1}{4}\right)^3 = \frac{1^3}{4^3} = \frac{1}{64}\). Next, take the square root of \(\frac{1}{64}\), which results in \(\sqrt{\frac{1}{64}} = \frac{1}{\sqrt{64}} = \frac{1}{8}\). So, the final answer is \(\frac{1}{8}\). Now, let’s have some fun with fractions! Did you know that when you're dealing with square roots and powers, you're essentially finding the balance between their magnitudes? It's like a mathematical dance! Watch out though: multiplying and dividing fractions can sometimes throw you off the beat, so keep those steps in check! And speaking of dance, learning about exponents and roots can be as rhythmic as a song! If you're intrigued by these number dance moves, you might enjoy diving deeper into algebraic expressions and how they relate to real-life scenarios, like computing areas or volumes! ✨