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Simplify this expression by using the negative rule of exponents

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 \(\frac{49}{4}\).

Would you like any more details or have any questions?

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)^{-

Learn how to simplify the expression \(\left(\frac{2}{7}\right)^{-2}\) using the negative exponent rule. Step-by-step solution provided with detailed explanations and related practice questions. Suitable for Grades 7-9.

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