`(-4)^(4)xx(5/4)^(4)=`_______

Options

A. `5^(4)`
B. `5^(-4)`
C. `4^(4)`
D. none of these

Answer

To solve the expression \((-4)^{4} \times \left(\frac{5}{4}\right)^{4}\), we can follow these steps:

### Step 1: Rewrite the expression
We start with the expression:
\[ (-4)^{4} \times \left(\frac{5}{4}\right)^{4} \]
We can rewrite \(-4\) as \(-1 \times 4\):
\[ (-1 \times 4)^{4} \times \left(\frac{5}{4}\right)^{4} \]

### Step 2: Apply the power of a product rule
Using the property of exponents \((a \times b)^{n} = a^{n} \times b^{n}\), we can separate the terms:
\[ (-1)^{4} \times (4)^{4} \times \left(\frac{5}{4}\right)^{4} \]

### Step 3: Apply the power of a quotient rule
Next, we can apply the property of exponents for the fraction:
\[ (-1)^{4} \times (4)^{4} \times \frac{5^{4}}{4^{4}} \]

### Step 4: Simplify the expression
Now, we can simplify the expression:
\[ (-1)^{4} \times \frac{(4)^{4} \times 5^{4}}{(4)^{4}} \]
The \(4^{4}\) in the numerator and denominator cancels out:
\[ (-1)^{4} \times 5^{4} \]

### Step 5: Evaluate \((-1)^{4}\)
Since \((-1)^{4} = 1\):
\[ 1 \times 5^{4} = 5^{4} \]

### Final Answer
Thus, the final answer is:
\[ 5^{4} \]