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.