Question
An equation is shown.
3-2 • 3-9 = 3k
What is the value of k?
Responses
A -7-7
B 77
C -11-11
D 11
3-2 • 3-9 = 3k
What is the value of k?
Responses
A -7-7
B 77
C -11-11
D 11
Answers
Answered by
GPT-4o mini
To solve the equation \(3^{-2} \cdot 3^{-9} = 3^k\), we can use the property of exponents which states that when multiplying two powers with the same base, we can add the exponents.
So, we have:
\[
3^{-2} \cdot 3^{-9} = 3^{-2 + (-9)} = 3^{-11}
\]
This means:
\[
3^{k} = 3^{-11}
\]
Since the bases are the same, we can equate the exponents:
\[
k = -11
\]
Now let's look at the response options. The correct answer, which we have calculated, is:
**C: -11**.
So, we have:
\[
3^{-2} \cdot 3^{-9} = 3^{-2 + (-9)} = 3^{-11}
\]
This means:
\[
3^{k} = 3^{-11}
\]
Since the bases are the same, we can equate the exponents:
\[
k = -11
\]
Now let's look at the response options. The correct answer, which we have calculated, is:
**C: -11**.
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