Express the following in exponential form
1250

Answer

To express 1250 in exponential form, we need to factor it into its prime factors. Here’s a step-by-step solution:

### Step 1: Prime Factorization
Start by dividing 1250 by the smallest prime number, which is 2.

- **Calculation**:
\[ 1250 \div 2 = 625 \]

### Step 2: Continue Factorization
Now, we need to factor 625. Since 625 is not divisible by 2, we try the next smallest prime number, which is 5.

- **Calculation**:
\[ 625 \div 5 = 125 \]

### Step 3: Factor 125
Next, we factor 125 by dividing it by 5 again.

- **Calculation**:
\[ 125 \div 5 = 25 \]

### Step 4: Factor 25
Now, we factor 25 by dividing it by 5 once more.

- **Calculation**:
\[ 25 \div 5 = 5 \]

### Step 5: Factor 5
Finally, we factor 5, which is already a prime number.

- **Calculation**:
\[ 5 \div 5 = 1 \]

### Step 6: Count the Prime Factors
Now, we can summarize the prime factors we found:
- We divided by 2 once, so we have \(2^1\).
- We divided by 5 four times, so we have \(5^4\).

### Step 7: Write in Exponential Form
Putting it all together, we can express 1250 in exponential form as:
\[ 1250 = 2^1 \times 5^4 \]

### Final Answer
Thus, the exponential form of 1250 is:
\[ 2^1 \times 5^4 \]

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