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

To calculate \( \left(\frac{1}{3}\right)^{4} \), you're raising the fraction \( \frac{1}{3} \) to the fourth power. This means you multiply \( \frac{1}{3} \) by itself four times: \[ \left(\frac{1}{3}\right)^{4} = \frac{1}{3} \times \frac{1}{3} \times \frac{1}{3} \times \frac{1}{3} = \frac{1^4}{3^4} = \frac{1}{81} \] So, \( \left(\frac{1}{3}\right)^{4} = \frac{1}{81} \). If you think of this fraction in terms of parts of a whole, raising it to a power shows how small each piece gets when you have to break it down into more and more parts! It’s kind of like cutting a pizza into smaller and smaller slices. The more slices you have, the smaller each slice becomes! Understanding the properties of exponents can help you solve many math problems more efficiently. For example, if you see an expression like \( \left(a^{m}\right)^{n} \), you can simply multiply the exponents, giving you \( a^{m \cdot n} \). Just remember that keeping track of the base is crucial, as getting mixed up can lead to all sorts of 'slice'-related slip-ups!