`(frac(-2)(3))^(2)=` ?

Options

A. (a) `frac(4)(3)`
B. (b) `frac(-2)(9)`
C. (c) `frac(4)(9)`
D. (d) `frac(-4)(9)`

Answer

To solve the expression \((\frac{-2}{3})^2\), we will follow these steps:

### Step 1: Write the expression
We start with the expression:
\[ \left(\frac{-2}{3}\right)^2 \]

### Step 2: Apply the exponent
When we raise a fraction to a power, we can apply the exponent to both the numerator and the denominator separately. Therefore, we can rewrite the expression as:
\[ \frac{(-2)^2}{3^2} \]

### Step 3: Calculate the numerator
Now, we calculate the square of the numerator:
\[ (-2)^2 = 4 \]

### Step 4: Calculate the denominator
Next, we calculate the square of the denominator:
\[ 3^2 = 9 \]

### Step 5: Combine the results
Now we can combine the results from the numerator and denominator:
\[ \frac{4}{9} \]

### Final Answer
Thus, the final answer is:
\[ \left(\frac{-2}{3}\right)^2 = \frac{4}{9} \]

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