To simplify the expression $\left(\frac{2}{7}\right)^{-2}$ using the negative exponent rule, follow these steps:

Step 1: Apply the Negative Exponent Rule

The negative exponent rule states that: $a^{-n} = \frac{1}{a^n}$ Applying this to the given expression: $\left(\frac{2}{7}\right)^{-2} = \frac{1}{\left(\frac{2}{7}\right)^2}$

Step 2: Simplify the Expression

Now, simplify the expression by squaring the fraction $\frac{2}{7}$: $\left(\frac{2}{7}\right)^2 = \frac{2^2}{7^2} = \frac{4}{49}$ So, the expression becomes: $\frac{1}{\frac{4}{49}}$

Step 3: Invert the Fraction

To simplify further, invert the fraction in the denominator: $\frac{1}{\frac{4}{49}} = \frac{49}{4}$

Thus, the simplified expression is $\frac{49}{4}$.

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Here are 5 related questions for further practice:

1. Simplify $\left(\frac{3}{5}\right)^{-3}$.
2. Evaluate $\left(\frac{4}{9}\right)^{-2}$.
3. Simplify the expression $\left(\frac{5}{2}\right)^{-1}$.
4. What is $\left(\frac{7}{4}\right)^{-2}$ in simplest form?
5. Simplify (\left(\frac{1}{3}\right)^{-