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Im a teacher Im seeing if this is correct

Let's solve the problem to confirm the correct answer.

The question asks to find which expression is equivalent to \( \left( \frac{2}{7} \right)^3 \).

To solve:

\[
\left( \frac{2}{7} \right)^3 = \frac{2^3}{7^3}
\]

Calculating each part:
- \( 2^3 = 8 \)
- \( 7^3 = 343 \)

Thus:

\[
\left( \frac{2}{7} \right)^3 = \frac{8}{343}
\]

Now, let's compare this with the answer choices:

1. \( \frac{2^3}{7^3} = \frac{8}{343} \) — This is correct.
2. \( \frac{2^3}{7} = \frac{8}{7} \) — Incorrect.
3. \( \frac{2}{7^3} = \frac{2}{343} \) — Incorrect.
4. \( \frac{6}{21} = \frac{2}{7} \) — Incorrect.

Therefore, the correct answer is the first option: \( \frac{2^3}{7^3} \).

Let me know if you need more details, and here are some related questions to explore:

1. How do you simplify expressions with exponents in fractions?
2. What happens when you raise a fraction to a negative power?
3. How do you compare two fractions with different denominators?
4. How does raising both the numerator and denominator to a power affect the fraction?
5. Can you explain the difference between raising the fraction and just raising the numerator or denominator?

**Tip**: When raising a fraction to a power, make sure both the numerator and denominator are raised to that power separately.

Which expression is equivalent to (2/7)^3?

Learn how to solve exponentiation of a fraction, specifically (2/7)^3. This problem focuses on applying the exponentiation rule to both the numerator and denominator of a fraction. Ideal for middle school students, Grades 6-8.

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