Question

Writing  Subtract 6.7 times 10 cubed minus 4 times 10 squared. Use pencil and paper. Describe the process of rewriting the numbers in this problem with the same power of 10.
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Part 1
6.7 times 10 cubed minus 4 times 10 squaredequals
  
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​(Use scientific notation. Use the multiplication symbol in the math palette as​ needed.)

Answer 1

To perform the subtraction \(6.7 \times 10^3 - 4 \times 10^2\), we first need to rewrite the numbers so that they have the same power of 10.

### Step 1: Rewrite \(4 \times 10^2\)

We want to express \(4 \times 10^2\) in terms of \(10^3\). Since \(10^3\) is \(10^2 \times 10^1\), we can convert \(4 \times 10^2\) to a form that uses \(10^3\).

\[
4 \times 10^2 = 4 \times 10^2 \times \frac{10^1}{10^1} = 4 \times \frac{10^3}{10} = \frac{4}{10} \times 10^3 = 0.4 \times 10^3
\]

### Step 2: Perform the subtraction

Now that both terms are expressed in the same power of 10, we can subtract:

\[
6.7 \times 10^3 - 0.4 \times 10^3
\]

Factoring out \(10^3\), we have:

\[
(6.7 - 0.4) \times 10^3 = 6.3 \times 10^3
\]

### Final Result

Thus, the answer is:

\[
6.7 \times 10^3 - 4 \times 10^2 = 6.3 \times 10^3
\]