Evaluate the following:
`(-13/12)^3`

Answer

To evaluate the expression \((-13/12)^3\), we will follow these steps:

### Step 1: Understand the expression
The expression \((-13/12)^3\) means that we need to cube the fraction \(-13/12\).

### Step 2: Apply the cube to the fraction
When we cube a fraction, we cube both the numerator and the denominator separately. Therefore:
\[ (-13/12)^3 = (-13)^3 / (12)^3 \]

### Step 3: Calculate the numerator
Now, we need to calculate \((-13)^3\):
\[ (-13)^3 = -13 \times -13 \times -13 \]
Calculating this step by step:
1. \(-13 \times -13 = 169\)
2. \(169 \times -13 = -2197\)

So, \((-13)^3 = -2197\).

### Step 4: Calculate the denominator
Next, we calculate \(12^3\):
\[ 12^3 = 12 \times 12 \times 12 \]
Calculating this step by step:
1. \(12 \times 12 = 144\)
2. \(144 \times 12 = 1728\)

So, \(12^3 = 1728\).

### Step 5: Combine the results
Now we can combine the results from the numerator and denominator:
\[ (-13/12)^3 = \frac{-2197}{1728} \]

### Final Answer
Thus, the final value of \((-13/12)^3\) is:
\[ \frac{-2197}{1728} \]

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