`(-(3)/(4))^(5)` is equal to

Options

A. `(81)/(256)`
B. `-(81)/(256)`
C. `-(243)/(1024)`
D. `(243)/(1024)`

Answer

To solve the expression \((- \frac{3}{4})^{5}\), we will follow these steps:

### Step 1: Understand the expression
The expression \((- \frac{3}{4})^{5}\) means we need to multiply \(- \frac{3}{4}\) by itself 5 times.

### Step 2: Write out the multiplication
\[ (- \frac{3}{4})^{5} = (- \frac{3}{4}) \times (- \frac{3}{4}) \times (- \frac{3}{4}) \times (- \frac{3}{4}) \times (- \frac{3}{4}) \]

### Step 3: Calculate the numerator
Now, we will calculate the numerator:
\[ (-3) \times (-3) \times (-3) \times (-3) \times (-3) = -3 \times -3 \times -3 \times -3 \times -3 \]
Since there are 5 negative signs, the product will be negative:
\[ (-3)^{5} = -243 \]

### Step 4: Calculate the denominator
Now, we will calculate the denominator:
\[ 4 \times 4 \times 4 \times 4 \times 4 = 4^{5} = 1024 \]

### Step 5: Combine the results
Now, we combine the results from the numerator and the denominator:
\[ (- \frac{3}{4})^{5} = \frac{-243}{1024} \]

### Final Answer
Thus, \((- \frac{3}{4})^{5} = \frac{-243}{1024}\).

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