Question

Click on ,begin emphasis,all,end emphasis, expressions equivalent to 200 left-parenthesis 10 Superscript x Baseline right-parenthesis.

Answer options with 5 options
1.
2 left-parenthesis 10 Superscript 2 x Baseline right-parenthesis

2.
2 left-parenthesis 10 Superscript 3 x Baseline right-parenthesis

3.
2 left-parenthesis 10 Superscript x plus 2 Baseline right-parenthesis

4.
20 left-parenthesis 10 Superscript 2 x Baseline right-parenthesis

5.
20 left-parenthesis 10 Superscript x plus 1 Baseline right-parenthesis

Answer 1

To find expressions equivalent to \( 200(10^x) \), let's first rewrite \( 200 \) in terms of powers of 10:

\[
200 = 2 \times 100 = 2 \times 10^2
\]

Thus, we can express \( 200(10^x) \) as:

\[
200(10^x) = (2 \times 10^2)(10^x) = 2(10^2 \times 10^x) = 2(10^{x+2})
\]

This means that \( 200(10^x) \) can be expressed as \( 2(10^{x + 2}) \).

Now let's evaluate the five given options:

1. \( 2(10^{2x}) \) - This is **not** equivalent because \( 2x \) is not the same as \( x + 2 \).

2. \( 2(10^{3x}) \) - This is **not** equivalent since \( 3x \) does not equal \( x + 2 \).

3. \( 2(10^{x + 2}) \) - This **is** equivalent since it matches our derived expression.

4. \( 20(10^{2x}) \) - This is **not** equivalent because \( 20 = 2 \times 10 \), and \( 10^{2x} \) does not match \( 10^{x + 2} \).

5. \( 20(10^{x + 1}) \) - This is **not** equivalent because even though \( 20 = 2 \times 10 \), \( 10^{x + 1} \) does not equal \( 10^{x + 2} \).

Thus, the only expression that is equivalent to \( 200(10^x) \) is:

**3. \( 2(10^{x + 2}) \)**.