Simplify : `((-5)^4)/( (-5)^2)`

Answer

To simplify the expression \(\frac{(-5)^4}{(-5)^2}\), we can follow these steps:

### Step 1: Identify the expression
We start with the expression:
\[ \frac{(-5)^4}{(-5)^2} \]

### Step 2: Apply the property of exponents
Using the property of exponents which states that \(\frac{a^m}{a^n} = a^{m-n}\), we can simplify the expression:
\[ \frac{(-5)^4}{(-5)^2} = (-5)^{4-2} \]

### Step 3: Simplify the exponent
Now we simplify the exponent:
\[ (-5)^{4-2} = (-5)^2 \]

### Step 4: Calculate \((-5)^2\)
Next, we calculate \((-5)^2\):
\[ (-5)^2 = (-5) \times (-5) = 25 \]

### Final Result
Thus, the simplified expression is:
\[ \frac{(-5)^4}{(-5)^2} = 25 \]

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