Which expression is equivalent to start fraction, 6, to the power minus 6 , divided by, 6, squared, end fraction, question mark

Question

6
2

6
−6

​
?
Answer
Multiple Choice Answers
6, to the power 46
4

start fraction, 1, divided by, 6, to the power 8 , end fraction
6
8

1
​

6, to the power 86
8

start fraction, 1, divided by, 6, cubed, end fraction
6
3

1
​

Answer 1

To simplify the expression \(\frac{6^{-6}}{6^{2}}\), we can use the properties of exponents.

1. Recall that when dividing numbers with the same base, we subtract the exponents: \[ \frac{a^m}{a^n} = a^{m-n} \]

2. Therefore, we can rewrite our expression: \[ \frac{6^{-6}}{6^2} = 6^{-6 - 2} = 6^{-8} \]

3. Now, we can express \(6^{-8}\) as a fraction: \[ 6^{-8} = \frac{1}{6^8} \]

Thus, the expression \(\frac{6^{-6}}{6^{2}}\) is equivalent to \( \frac{1}{6^8} \).

Looking at the multiple choice answers, the correct answer is: \[ \frac{1}{6^8} \]