Evaluate :
` ((-3)/(4))^(5)`

Answer

To evaluate \((-3/4)^5\), follow these steps:

### Step 1: Write the expression in expanded form
The expression \((-3/4)^5\) means multiplying \(-3/4\) by itself 5 times. Therefore, we can write it as:
\[ (-3/4) \times (-3/4) \times (-3/4) \times (-3/4) \times (-3/4) \]

### Step 2: Separate the numerators and denominators
We can separate the multiplication of the numerators and the denominators:
\[ = \frac{(-3) \times (-3) \times (-3) \times (-3) \times (-3)}{4 \times 4 \times 4 \times 4 \times 4} \]

### Step 3: Calculate the numerator
Now, calculate the numerator:
\[ (-3) \times (-3) \times (-3) \times (-3) \times (-3) = (-3)^5 \]
Calculating \((-3)^5\):
\[ (-3) \times (-3) = 9 \\ 9 \times (-3) = -27 \\ -27 \times (-3) = 81 \\ 81 \times (-3) = -243 \]
So, \((-3)^5 = -243\).

### Step 4: Calculate the denominator
Now, calculate the denominator:
\[ 4 \times 4 \times 4 \times 4 \times 4 = 4^5 \]
Calculating \(4^5\):
\[ 4 \times 4 = 16 \\ 16 \times 4 = 64 \\ 64 \times 4 = 256 \\ 256 \times 4 = 1024 \]
So, \(4^5 = 1024\).

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

### Final Answer
Thus, the evaluated result of \((-3/4)^5\) is:
\[ \frac{-243}{1024} \]

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