Evaluate: `(5^(7)-:5^(6))^(2)=`____________

Options

A. `5^(1)`
B. `5^(4)`
C. `5^(3)`
D. `5^(2)`

Answer

To evaluate the expression \((5^{7} \div 5^{6})^{2}\), we can follow these steps:

### Step 1: Apply the property of exponents for division
Using the property of exponents that states \(\frac{a^m}{a^n} = a^{m-n}\), we can simplify the expression inside the parentheses:

\[ 5^{7} \div 5^{6} = 5^{7-6} = 5^{1} \]

### Step 2: Substitute back into the expression
Now, we substitute \(5^{1}\) back into the original expression:

\[ (5^{1})^{2} \]

### Step 3: Apply the property of exponents for powers
Using the property that states \((a^m)^n = a^{m \cdot n}\), we can simplify further:

\[ (5^{1})^{2} = 5^{1 \cdot 2} = 5^{2} \]

### Step 4: Calculate \(5^{2}\)
Now we calculate \(5^{2}\):

\[ 5^{2} = 5 \times 5 = 25 \]

### Final Answer
Thus, the evaluated expression is:

\[ \boxed{25} \]