Question

An equation is shown.



3^-2 • 3^-9 = 3^k

What is the value of k?
Responses
A -7
B 7
C -11
D 11

Answer 1

To solve the equation \(3^{-2} \cdot 3^{-9} = 3^k\), we can use the property of exponents that states \(a^m \cdot a^n = a^{m+n}\).

So, we can combine the exponents on the left side:

\[
3^{-2} \cdot 3^{-9} = 3^{-2 + (-9)} = 3^{-2 - 9} = 3^{-11}
\]

Now we have:

\[
3^{-11} = 3^k
\]

Since the bases are the same, we can set the exponents equal to each other:

\[
k = -11
\]

Thus, the value of \(k\) is \(-11\).

The correct response is:

**C -11**