Marsh Chen
11/29/2023 · Senior High School
Complete this assessment to review what you've learned. It will not count toward your grade. Apply the Properties of Integer Exponents to generate equivalent expressions to \( 3^{7} \cdot 3^{-9} \) with only positive exponents, then solve the expression. Your answer will be a simplified fraction with no remaining exponents. (1 point) \( 3^{7} \cdot 3^{-9}= \) Check answer Remaining Attempts : 3
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Tutor-Verified Answer
Step-by-step Solution
To simplify the expression \( 3^{7} \cdot 3^{-9} \) using the properties of integer exponents, we can apply the property that states \( a^m \cdot a^n = a^{m+n} \).
So, we have:
\[
3^{7} \cdot 3^{-9} = 3^{7 + (-9)} = 3^{7 - 9} = 3^{-2}
\]
Now, to express \( 3^{-2} \) with only positive exponents, we can use the property that \( a^{-n} = \frac{1}{a^n} \):
\[
3^{-2} = \frac{1}{3^{2}}
\]
Now, we can simplify \( 3^{2} \):
\[
3^{2} = 9
\]
Thus, we have:
\[
3^{-2} = \frac{1}{9}
\]
So, the final answer is:
\[
3^{7} \cdot 3^{-9} = \frac{1}{9}
\]
Quick Answer
\( 3^{7} \cdot 3^{-9} = \frac{1}{9} \)
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