How many times larger is 9×10^−8

Question

than  3×10^−12
?(2 points)
Responses

6×10−4
6 times 10 to the negative 4 power

6×10−3
6 times 10 to the negative 3 power

3×103
3 times 10 cubed

3×104
3 times 10 to the 4th power
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Answer 1

To find out how many times larger \( 9 \times 10^{-8} \) is than \( 3 \times 10^{-12} \), we divide the two numbers:

\[ \frac{9 \times 10^{-8}}{3 \times 10^{-12}} \]

First, divide the coefficients:

\[ \frac{9}{3} = 3 \]

Next, to handle the powers of 10, we apply the rule of exponents that states \( \frac{10^a}{10^b} = 10^{a-b} \):

\[ \frac{10^{-8}}{10^{-12}} = 10^{-8 - (-12)} = 10^{-8 + 12} = 10^{4} \]

Now, we combine the results:

\[ 3 \times 10^4 \]

Thus, \( 9 \times 10^{-8} \) is \( 3 \times 10^{4} \) times larger than \( 3 \times 10^{-12} \).

The correct response is:

3×10⁴ (3 times 10 to the 4th power)