Evaluate. Write your answer as a fraction in simplest form. \( \left(\frac{1}{2}\right)^{4} \)
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To evaluate \( \left(\frac{1}{2}\right)^{4} \), you multiply \( \frac{1}{2} \) by itself four times: \[ \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} = \frac{1 \times 1 \times 1 \times 1}{2 \times 2 \times 2 \times 2} = \frac{1}{16}. \] So, the answer is \( \frac{1}{16} \). Now for some extra fun facts! Back in ancient times, fractions were quite the brain teaser! The Egyptians were among the first to document fractions, using them for practical purposes like land measurement and grain distribution. They essentially had a fraction system that only dealt with unit fractions, which means they expressed all fractions as sums of fractions with 1 in the numerator. Nit-picking over decimal points might be modern, but did you know that the concept of fractions is a stepping stone to understanding ratios, percentages, and even algebra? So when you're working with fractions, you're sharpening your math skills for a plethora of applications, from cooking and budgeting to engineering and statistics! Fun, right?
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