Question

Question
What power of 10 would make the following equation true?

3.75 × 10^? = 0.0000375


(1 point)
Responses:

-6
-6

5
5

-7
-7

6
6

7
7

-5

Answer 1

To solve the equation \( 3.75 \times 10^? = 0.0000375 \), we need to express \( 0.0000375 \) in a form that makes it easier to compare with \( 3.75 \).

First, we can convert \( 0.0000375 \) to scientific notation:

1. Move the decimal point in \( 0.0000375 \) to the right 5 places to get \( 3.75 \).
2. Since we moved the decimal 5 places to the right, we will use a negative exponent of \( -5 \):
\[
0.0000375 = 3.75 \times 10^{-5}
\]

Now, we equate both sides of the original equation:

\[
3.75 \times 10^? = 3.75 \times 10^{-5}
\]

From this equation, we can see that:

\[
10^? = 10^{-5}
\]

This implies:

\[
? = -5
\]

So, the power of 10 that makes the equation true is **-5**.

Thus, the correct response is: **-5**.