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The given expression is:

\[
\frac{49}{18} \times \left(\frac{9}{14}\right)^2
\]

Let's solve this step by step.

### Step 1: Simplify \(\frac{9}{14}\)
- The fraction \(\frac{9}{14}\) cannot be simplified further.

### Step 2: Square the Fraction
- Square the fraction \(\left(\frac{9}{14}\right)^2\):

\[
\left(\frac{9}{14}\right)^2 = \frac{9^2}{14^2} = \frac{81}{196}
\]

### Step 3: Multiply the Fractions
- Multiply \(\frac{49}{18}\) by \(\frac{81}{196}\):

\[
\frac{49}{18} \times \frac{81}{196} = \frac{49 \times 81}{18 \times 196}
\]

### Step 4: Simplify the Result
- Simplify the product of the numerators and denominators:

\[
49 \times 81 = 3969
\]

\[
18 \times 196 = 3528
\]

So, the expression simplifies to:

\[
\frac{3969}{3528}
\]

Next, simplify \(\frac{3969}{3528}\) by finding the greatest common divisor (GCD) of 3969 and 3528.

- The GCD of 3969 and 3528 is 441.

So:

\[
\frac{3969 \div 441}{3528 \div 441} = \frac{9}{8}
\]

### Final Answer
The simplified result of the given expression is:

\[
\boxed{\frac{9}{8}}
\]

Would you like further details on any of the steps? Here are some related questions:

1. What is the process to find the greatest common divisor (GCD)?
2. How do you simplify fractions involving squares?
3. What are the properties of multiplying fractions?
4. Can we simplify square roots of fractions in a similar way?
5. How does squaring a fraction affect its value?

**Tip:** When multiplying fractions, always check if you can simplify before multiplying to make calculations easier!

Simplify the expression (49/18) * (9/14)^2

Learn how to simplify the fractional expression (49/18) * (9/14)^2 using multiplication and exponentiation. This step-by-step guide covers key concepts in fraction manipulation for students in Grades 6-8.

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