How many digits are there in `2^(10)xx5^(8)` ?

Options

A. A)8
B. B)9
C. C)10
D. D)18

Answer

To find out how many digits are in the expression \(2^{10} \times 5^{8}\), we can follow these steps:

### Step 1: Rewrite the expression
We start with the expression:
\[ 2^{10} \times 5^{8} \]
We can separate \(2^{10}\) into \(2^{8} \times 2^{2}\):
\[ 2^{10} \times 5^{8} = (2^{8} \times 5^{8}) \times 2^{2} \]

### Step 2: Simplify the expression
Now, we can simplify \(2^{8} \times 5^{8}\) as follows:
\[ 2^{8} \times 5^{8} = (2 \times 5)^{8} = 10^{8} \]
So, we rewrite the expression:
\[ (10^{8}) \times 2^{2} \]

### Step 3: Calculate \(2^{2}\)
Next, we calculate \(2^{2}\):
\[ 2^{2} = 4 \]
Thus, we can rewrite our expression as:
\[ 10^{8} \times 4 \]

### Step 4: Calculate the final value
Now we can calculate \(10^{8} \times 4\):
\[ 10^{8} \times 4 = 4 \times 10^{8} = 400000000 \]

### Step 5: Count the digits
To find the number of digits in \(400000000\), we can see that it consists of the digit '4' followed by 8 zeros. Therefore, the total number of digits is:
\[ 1 \text{ (for '4')} + 8 \text{ (for the zeros)} = 9 \]

### Final Answer
Thus, the total number of digits in \(2^{10} \times 5^{8}\) is:
\[ \boxed{9} \]

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