`(14.96 xx 10^(10)) - (3.84 xx 10^(8))` is expressed in standard form as

Options

A. `1492.16 xx 10^(8)`
B. `1.49216 xx 10^(11)`
C. `149216 xx 10^(9)`
D. `14.9216 xx 10^(10)`

Answer

To solve the expression \((14.96 \times 10^{10}) - (3.84 \times 10^{8})\) and express it in standard form, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Terms**: We have two terms:
- \(A = 14.96 \times 10^{10}\)
- \(B = 3.84 \times 10^{8}\)

2. **Align the Powers of 10**: To subtract these two terms, we need to express them with the same power of 10. We can convert \(A\) to have the same power as \(B\):
\[ A = 14.96 \times 10^{10} = 14.96 \times 10^{2} \times 10^{8} = 1496 \times 10^{8} \]
Now we have:
- \(A = 1496 \times 10^{8}\)
- \(B = 3.84 \times 10^{8}\)

3. **Perform the Subtraction**: Now we can subtract \(B\) from \(A\):
\[ A - B = (1496 - 3.84) \times 10^{8} = 1492.16 \times 10^{8} \]

4. **Convert to Standard Form**: The standard form requires that the number is expressed as \(N \times 10^{k}\) where \(1 \leq N < 10\). We need to adjust \(1492.16\):
\[ 1492.16 = 1.49216 \times 10^{3} \]
Therefore:
\[ 1492.16 \times 10^{8} = 1.49216 \times 10^{3} \times 10^{8} = 1.49216 \times 10^{11} \]

5. **Final Result**: Thus, the expression \((14.96 \times 10^{10}) - (3.84 \times 10^{8})\) in standard form is:
\[ 1.49216 \times 10^{11} \]