The expression \(\left(\frac{2}{7}\right)^{-3}\) can be simplified using the negative exponent rule, which states that \(a^{-n} = \frac{1}{a^n}\). 

So, applying this rule:

\[
\left(\frac{2}{7}\right)^{-3} = \frac{1}{\left(\frac{2}{7}\right)^3}
\]

Now, calculate \(\left(\frac{2}{7}\right)^3\):

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

Thus:

\[
\left(\frac{2}{7}\right)^{-3} = \frac{1}{\frac{8}{343}} = \frac{343}{8}
\]

So, the simplified result is:

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

Would you like any further explanation or details?

Here are 5 related questions:
1. What is the rule for handling negative exponents?
2. How do you simplify fractional powers with negative exponents?
3. Can you solve \(\left(\frac{5}{6}\right)^{-2}\)?
4. How do you simplify \(\left(\frac{4}{9}\right)^{\frac{3}{2}}\)?
5. How do negative exponents affect the base number?

**Tip:** Negative exponents indicate reciprocals. To simplify, flip the fraction and apply the positive exponent.

Learn how to simplify the expression (2/7)^-3 using the negative exponent rule. This problem involves key concepts like exponents and fractions. Step-by-step solution provided, suitable for students in Grades 6-8.

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