Which expression is equivalent to 5, to the power minus 6 , dot, 5, to the power minus 1 , question mark5

Question

−6
⋅5
−1
?
Answer
Multiple Choice Answers
start fraction, 1, divided by, 5, to the power 7 , end fraction
5
7

1
​

5, to the power 75
7

start fraction, 1, divided by, 5, to the power 5 , end fraction
5
5

1
​

start fraction, 1, divided by, 5, to the power 8 , end fraction
5
8

1
​

Answer 1

To simplify the expression \(5^{-6} \cdot 5^{-1}\), we can apply the property of exponents that states \(a^m \cdot a^n = a^{m+n}\).

So, we have: \[ 5^{-6} \cdot 5^{-1} = 5^{-6 + (-1)} = 5^{-7} \]

Now, we can express \(5^{-7}\) in fractional form: \[ 5^{-7} = \frac{1}{5^7} \]

Thus, the equivalent expression is: \[ \frac{1}{5^7} \]

Looking at the answer choices, the correct one is: \[ \frac{1}{5^7} \]