Question
Which expression is equivalent to left parenthesis, 6, squared, dot, 6, to the power 5 , right parenthesis, to the power minus 6 , question mark(6
2
⋅6
5
)
−6
?
Answer
Multiple Choice Answers
6, to the power minus 426
−42
6, to the power minus 366
−36
6, to the power 426
42
6, to the power minus 606
−60
2
⋅6
5
)
−6
?
Answer
Multiple Choice Answers
6, to the power minus 426
−42
6, to the power minus 366
−36
6, to the power 426
42
6, to the power minus 606
−60
Answers
GPT-4o mini
To simplify the expression \((6^2 \cdot 6^5)^{-6}\), we first apply the property of exponents that allows us to combine the terms inside the parentheses:
\[
6^2 \cdot 6^5 = 6^{2+5} = 6^7
\]
Next, we apply the exponent \(-6\) to the result:
\[
(6^7)^{-6} = 6^{7 \cdot -6} = 6^{-42}
\]
Now, we can identify the equivalent expression from the given multiple-choice answers.
Thus, the answer is:
\[
6^{-42}
\]
So, the correct option is:
**6, to the power minus 42 (−42)**.
\[
6^2 \cdot 6^5 = 6^{2+5} = 6^7
\]
Next, we apply the exponent \(-6\) to the result:
\[
(6^7)^{-6} = 6^{7 \cdot -6} = 6^{-42}
\]
Now, we can identify the equivalent expression from the given multiple-choice answers.
Thus, the answer is:
\[
6^{-42}
\]
So, the correct option is:
**6, to the power minus 42 (−42)**.