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

Question

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

Answer 1

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).