Evaluate the following:
`(9/7)^3`

Answer

To evaluate \((\frac{9}{7})^3\), we can follow these steps:

### Step 1: Write the expression
We start with the expression:
\[ \left(\frac{9}{7}\right)^3 \]

### Step 2: Apply the power to the numerator and denominator
Using the property of exponents that states \((\frac{a}{b})^n = \frac{a^n}{b^n}\), we can rewrite the expression as:
\[ \frac{9^3}{7^3} \]

### Step 3: Calculate \(9^3\)
Now we calculate \(9^3\):
\[ 9^3 = 9 \times 9 \times 9 \]
Calculating step-by-step:
- \(9 \times 9 = 81\)
- \(81 \times 9 = 729\)

Thus, \(9^3 = 729\).

### Step 4: Calculate \(7^3\)
Next, we calculate \(7^3\):
\[ 7^3 = 7 \times 7 \times 7 \]
Calculating step-by-step:
- \(7 \times 7 = 49\)
- \(49 \times 7 = 343\)

Thus, \(7^3 = 343\).

### Step 5: Combine the results
Now we can combine the results from steps 3 and 4:
\[ \left(\frac{9}{7}\right)^3 = \frac{729}{343} \]

### Final Answer
Thus, the value of \((\frac{9}{7})^3\) is:
\[ \frac{729}{343} \]

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