If `5^a =3125`, then the value of `5^(a-3)` is

Options

A. 25
B. 125
C. 625
D. 1625

Answer

To solve the equation \(5^a = 3125\) and find the value of \(5^{(a-3)}\), we can follow these steps:

### Step 1: Rewrite 3125 as a power of 5
We need to express 3125 in terms of base 5. We can do this by calculating powers of 5:
- \(5^1 = 5\)
- \(5^2 = 25\)
- \(5^3 = 125\)
- \(5^4 = 625\)
- \(5^5 = 3125\)

From this, we can see that:
\[ 3125 = 5^5 \]

### Step 2: Set the exponents equal
Since we have \(5^a = 5^5\), we can set the exponents equal to each other:
\[ a = 5 \]

### Step 3: Substitute \(a\) into \(5^{(a-3)}\)
Now that we know \(a = 5\), we can substitute this value into the expression \(5^{(a-3)}\):
\[ 5^{(a-3)} = 5^{(5-3)} = 5^2 \]

### Step 4: Calculate \(5^2\)
Now we calculate \(5^2\):
\[ 5^2 = 25 \]

### Final Answer
Thus, the value of \(5^{(a-3)}\) is:
\[ \boxed{25} \]