`(2.4xx10^(3))-:(8xx10^(-2))` equals

Options

A. `3xx10^(5)`
B. `3xx10^(4)`
C. `3xx10^(-5)`
D. `30`

Answer

To solve the expression \((2.4 \times 10^{3}) \div (8 \times 10^{-2})\), we can follow these steps:

### Step 1: Rewrite the expression
We start with the expression:
\[ \frac{2.4 \times 10^{3}}{8 \times 10^{-2}} \]

### Step 2: Separate the coefficients and the powers of ten
We can separate the coefficients (the numbers in front) and the powers of ten:
\[ \frac{2.4}{8} \times \frac{10^{3}}{10^{-2}} \]

### Step 3: Calculate the coefficient
Now, we calculate \(\frac{2.4}{8}\):
\[ \frac{2.4}{8} = 0.3 \]

### Step 4: Simplify the powers of ten
Next, we simplify the powers of ten using the property of exponents:
\[ \frac{10^{3}}{10^{-2}} = 10^{3 - (-2)} = 10^{3 + 2} = 10^{5} \]

### Step 5: Combine the results
Now we combine the results from Step 3 and Step 4:
\[ 0.3 \times 10^{5} \]

### Step 6: Convert to standard form
To express \(0.3 \times 10^{5}\) in standard scientific notation, we can rewrite \(0.3\) as \(3.0 \times 10^{-1}\):
\[ 0.3 \times 10^{5} = 3.0 \times 10^{-1} \times 10^{5} = 3.0 \times 10^{4} \]

### Final Answer
Thus, the final answer is:
\[ 3.0 \times 10^{4} \]

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