Question
Choose the expression that is equivalent to the quantity 9 raised to the negative second power times 9 raised to the seventh power end quantity all raised to the negative third power
−99
negative 1 divided by 9 raised to the sixth power
1 divided by 9 raised to the fifteenth power
927
−99
negative 1 divided by 9 raised to the sixth power
1 divided by 9 raised to the fifteenth power
927
Answers
GPT-4o mini
To simplify the expression \( (9^{-2} \times 9^{7})^{-3} \), we can follow these steps:
1. Use the property of exponents that states \( a^m \times a^n = a^{m+n} \):
\[
9^{-2} \times 9^{7} = 9^{-2 + 7} = 9^{5}
\]
2. Now, take this result and raise it to the power of \(-3\):
\[
(9^{5})^{-3} = 9^{5 \times -3} = 9^{-15}
\]
3. Finally, we can express \( 9^{-15} \) as:
\[
9^{-15} = \frac{1}{9^{15}}
\]
So the expression \( (9^{-2} \times 9^{7})^{-3} \) simplifies to \( \frac{1}{9^{15}} \).
Thus, the correct equivalent expression is:
\[
\frac{1}{9^{15}}
\]
Therefore, the answer is:
**1 divided by 9 raised to the fifteenth power**.
1. Use the property of exponents that states \( a^m \times a^n = a^{m+n} \):
\[
9^{-2} \times 9^{7} = 9^{-2 + 7} = 9^{5}
\]
2. Now, take this result and raise it to the power of \(-3\):
\[
(9^{5})^{-3} = 9^{5 \times -3} = 9^{-15}
\]
3. Finally, we can express \( 9^{-15} \) as:
\[
9^{-15} = \frac{1}{9^{15}}
\]
So the expression \( (9^{-2} \times 9^{7})^{-3} \) simplifies to \( \frac{1}{9^{15}} \).
Thus, the correct equivalent expression is:
\[
\frac{1}{9^{15}}
\]
Therefore, the answer is:
**1 divided by 9 raised to the fifteenth power**.