Solve the following expressions .
`3^(-3) + (-3)^3`

Answer

To solve the expression \( 3^{-3} + (-3)^3 \), we will follow these steps:

### Step 1: Evaluate \( 3^{-3} \)
Using the property of exponents, we know that:
\[ a^{-n} = \frac{1}{a^n} \]
So, we can rewrite \( 3^{-3} \) as:
\[ 3^{-3} = \frac{1}{3^3} \]
Now, calculate \( 3^3 \):
\[ 3^3 = 3 \times 3 \times 3 = 27 \]
Thus, we have:
\[ 3^{-3} = \frac{1}{27} \]

### Step 2: Evaluate \( (-3)^3 \)
Now, we calculate \( (-3)^3 \):
\[ (-3)^3 = (-3) \times (-3) \times (-3) \]
Calculating this step-by-step:
- First, \( (-3) \times (-3) = 9 \)
- Then, \( 9 \times (-3) = -27 \)

So, we have:
\[ (-3)^3 = -27 \]

### Step 3: Combine the results
Now we can combine the results from Step 1 and Step 2:
\[ 3^{-3} + (-3)^3 = \frac{1}{27} + (-27) \]
To add these two terms, we need a common denominator. The common denominator here is 27. We can rewrite \(-27\) as:
\[ -27 = \frac{-27 \times 27}{27} = \frac{-729}{27} \]
Now we can add:
\[ \frac{1}{27} + \frac{-729}{27} = \frac{1 - 729}{27} = \frac{-728}{27} \]

### Final Answer
Thus, the final answer is:
\[ \frac{-728}{27} \]

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