Question

Find the product. You must show ALL work to earn full credit.

6 x10^4 and 8 x 10^10
explain it in numbers so I can understand

Answer 1

To multiply \(6 \times 10^4\) and \(8 \times 10^{10}\), we can follow a systematic approach. Here's how you can do it step by step:

### Step 1: Write the numbers in a clear format
We have:
- First number: \(6 \times 10^4\)
- Second number: \(8 \times 10^{10}\)

### Step 2: Multiply the coefficients
The coefficients here are \(6\) and \(8\). We will multiply these two numbers together.
\[
6 \times 8 = 48
\]

### Step 3: Multiply the powers of ten
Next, we need to multiply the \(10^4\) and \(10^{10}\) components. When you multiply numbers with the same base (in this case, base 10), you add the exponents:
\[
10^4 \times 10^{10} = 10^{4 + 10} = 10^{14}
\]

### Step 4: Combine the results
Now that we have both the product of the coefficients and the power of ten, we can combine them:
\[
48 \times 10^{14}
\]

### Step 5: Final representation
The product of \(6 \times 10^4\) and \(8 \times 10^{10}\) is:
\[
48 \times 10^{14}
\]

### Step 6: Scientific notation (optional)
If we want to express \(48 \times 10^{14}\) in proper scientific notation, we must ensure the coefficient is between \(1\) and \(10\). Since \(48\) is not in this range, we can rewrite it as:
\[
4.8 \times 10^1 \times 10^{14}
\]

Now, we combine the powers of ten:
\[
4.8 \times 10^{1 + 14} = 4.8 \times 10^{15}
\]

### Final Answer
Thus, the final product of \(6 \times 10^4\) and \(8 \times 10^{10}\) is:
\[
4.8 \times 10^{15}
\]