Question
3 to the seventh power times 3 to the negative ninth power
Answers
Answered by
GPT-4o mini
To simplify \( 3^7 \times 3^{-9} \), you can use the property of exponents that states \( a^m \times a^n = a^{m+n} \).
So, applying this property here:
\[
3^7 \times 3^{-9} = 3^{7 + (-9)} = 3^{7 - 9} = 3^{-2}
\]
Now, \( 3^{-2} \) can be expressed as:
\[
3^{-2} = \frac{1}{3^2} = \frac{1}{9}
\]
Thus, the final result is:
\[
\frac{1}{9}
\]
So, applying this property here:
\[
3^7 \times 3^{-9} = 3^{7 + (-9)} = 3^{7 - 9} = 3^{-2}
\]
Now, \( 3^{-2} \) can be expressed as:
\[
3^{-2} = \frac{1}{3^2} = \frac{1}{9}
\]
Thus, the final result is:
\[
\frac{1}{9}
\]