To solve \(\left(\frac{1}{10,000}\right)^{\frac{3}{4}}\), let's break it down step by step:

1. The number \(10,000\) can be written as \(10^4\), since \(10^4 = 10,000\).
   
   Therefore, \(\frac{1}{10,000}\) becomes \(10^{-4}\).

2. Now we raise this to the power of \(\frac{3}{4}\):
   \[
   (10^{-4})^{\frac{3}{4}} = 10^{-4 \times \frac{3}{4}} = 10^{-3}.
   \]

3. The result is:
   \[
   10^{-3} = \frac{1}{10^3} = \frac{1}{1000}.
   \]

Thus, \(\left(\frac{1}{10,000}\right)^{\frac{3}{4}} = \frac{1}{1000}\).

Would you like more details on any step? Here are some related questions:

1. How would you simplify expressions involving fractional exponents?
2. What is the general rule for raising powers to a power?
3. How do you convert large numbers into powers of 10?
4. How does changing the exponent affect the magnitude of the result?
5. How do fractional exponents relate to roots and powers?

**Tip:** When dealing with exponents, always try to express the base in terms of powers of 10 if possible—it simplifies calculations significantly.

Learn how to simplify (1/10,000) raised to the power of 3/4 in this step-by-step guide. This problem explores key concepts such as fractional exponents, powers of ten, and the laws of exponents. Suitable for students in Grades 8-10.

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