`(0.1 xx 0.01 xx 0.001 xx 10^(7))` is equal to

Options

A. 100
B. `(1)/(10)`
C. `(1)/(100)`
D. 10

Answer

To solve the expression \( (0.1 \times 0.01 \times 0.001 \times 10^{7}) \), we will follow these steps:

### Step 1: Convert decimals to powers of 10
First, we convert each decimal into its equivalent power of 10:
- \( 0.1 = 10^{-1} \)
- \( 0.01 = 10^{-2} \)
- \( 0.001 = 10^{-3} \)

So, we can rewrite the expression as:
\[ (10^{-1} \times 10^{-2} \times 10^{-3} \times 10^{7}) \]

### Step 2: Combine the powers of 10
When multiplying numbers with the same base, we add their exponents:
\[ 10^{-1} \times 10^{-2} \times 10^{-3} \times 10^{7} = 10^{-1 + (-2) + (-3) + 7} \]

### Step 3: Simplify the exponent
Now, we simplify the exponent:
\[ -1 - 2 - 3 + 7 = -6 + 7 = 1 \]
Thus, we have:
\[ 10^{1} \]

### Step 4: Calculate the final result
Now, we can evaluate \( 10^{1} \):
\[ 10^{1} = 10 \]

### Final Answer
The value of \( (0.1 \times 0.01 \times 0.001 \times 10^{7}) \) is \( 10 \).

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