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The problem asks which expression is equivalent to \(\left(\frac{m}{d}\right)^{\frac{n}{d}}\).

Let's simplify this expression step-by-step:

1. **Given Expression**:
   \[
   \left(\frac{m}{d}\right)^{\frac{n}{d}}
   \]

2. **Apply the Power Rule**:
   The power rule states that \(\left(\frac{a}{b}\right)^c = \frac{a^c}{b^c}\). Applying this rule, we get:
   \[
   \left(\frac{m}{d}\right)^{\frac{n}{d}} = \frac{m^{\frac{n}{d}}}{d^{\frac{n}{d}}}.
   \]

3. **Rewriting in terms of other options**:
   - This expression matches the form of the answer choice \(\left(m^n\right)^{\frac{1}{d}}\).

So, the correct equivalent expression is:

**\(\left(m^n\right)^{\frac{1}{d}}\)**.

Would you like further details or have any questions? 

Here are some related questions:
1. What is the Power Rule in exponents?
2. How can we simplify an expression with fractional exponents?
3. What other equivalent forms can \(\left(\frac{m}{d}\right)^{\frac{n}{d}}\) take?
4. How do exponent rules apply when dealing with fractions?
5. Can this simplification be applied in real-world situations?

**Tip:** Always start by applying exponent rules step-by-step to simplify expressions.

Which of the following are equivalent to the expression (m/d)^(n/d)? Select all that apply.

Explore how to simplify expressions involving fractional exponents, specifically (m/d)^(n/d). Learn step-by-step solutions using exponent rules, including the power of a quotient property and properties of exponents. Suitable for high school students in Grades 9-11.

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