Which expression is equivalent to start fraction, 5, to the power minus 1 , divided by, 5, to the power minus 2 , end fraction, question mark

Question

5
−2

5
−1

​
?
Answer
Multiple Choice Answers
start fraction, 1, divided by, 5, cubed, end fraction
5
3

1
​

5, cubed5
3

55
start fraction, 1, divided by, 5, squared, end fraction
5
2

1
​

Answer 1

To simplify the expression \(\frac{5^{-1}}{5^{-2}}\), we can use the properties of exponents.

When dividing two exponential expressions with the same base, we can subtract the exponents:

\[ \frac{a^m}{a^n} = a^{m-n} \]

Here, we have:

\[ \frac{5^{-1}}{5^{-2}} = 5^{-1 - (-2)} = 5^{-1 + 2} = 5^{1} \]

Now, \(5^{1} = 5\).

None of the provided multiple-choice answers are equivalent to \(5\). However, if the question asked for the reciprocal or an expression that simplifies further, we can express \(5\) in terms of negative exponents too:

To represent \(5\) as a fraction, we recall:

\[ 5 = \frac{5^3}{5^3} = \frac{5^3}{5^2 \cdot 5} = \frac{1}{5^{-1}} \]

But that would be unnecessary here.

Among the provided choices:

1. \(\frac{1}{5^3}\)
2. \(5^3\)
3. \(\frac{1}{5^2}\)

None of them are direct representations of your original fraction after simplification.

The correct answer based on your expression \(\frac{5^{-1}}{5^{-2}} = 5^{1} = 5\) is not present in the options.