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The question asks for the repeated multiplication form of \(\left(-\frac{1}{3}\right)^4\). To convert this into repeated multiplication, we expand the expression \(\left(-\frac{1}{3}\right)^4\) as a product of four identical terms.

This means:
\[
\left(-\frac{1}{3}\right)^4 = \left(-\frac{1}{3}\right) \times \left(-\frac{1}{3}\right) \times \left(-\frac{1}{3}\right) \times \left(-\frac{1}{3}\right)
\]

Thus, the correct choice in the image should be the option that represents this repeated multiplication form. Let's analyze the given options:

- **Option A**: Includes \(\left(-\frac{1}{3}\right)^4\) in several places, which doesn't match the expanded form.
- **Option B**: Same as A, with powers of 4 still present.
- **Option C**: Expands correctly as \(\left(-\frac{1}{3}\right) \times \left(-\frac{1}{3}\right) \times \left(-\frac{1}{3}\right) \times \left(-\frac{1}{3}\right)\). This matches the desired expression.
- **Option D**: Incorrect arrangement of terms, as it includes incorrect negative signs and lacks proper grouping.
- **Option E**: Also incorrect as it omits the negative sign.

The correct answer is **Option C**.

Would you like further details or have any questions about this?

Here are five related questions to expand your understanding:
1. How would \(\left(-\frac{1}{3}\right)^5\) be written in repeated multiplication form?
2. What is the result of \(\left(-\frac{1}{3}\right)^4\) in decimal form?
3. How do exponents affect the signs in repeated multiplication when the base is negative?
4. Can you expand \(\left(-2\right)^3\) into repeated multiplication?
5. How do fractional exponents differ from whole number exponents?

**Tip**: When the base is negative, the exponent's parity (odd or even) will determine whether the final result is positive or negative.

Convert the expression (-1/3)^4 into repeated multiplication form.

Learn how to express (-1/3)^4 as a repeated multiplication. This problem demonstrates key exponent rules and the correct method to expand negative fractional bases. Suitable for students in Grades 6-8.

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