Which expression is equivalent to 5, to the power minus 2 , times, 5, to the power 5 , question mark5

Question

−2
×5
5
?
Answer
Multiple Choice Answers
start fraction, 1, divided by, 5, to the power 10 , end fraction
5
10

1
​

5, cubed5
3

start fraction, 1, divided by, 5, cubed, end fraction
5
3

1
​

start fraction, 1, divided by, 5, to the power 7 , end fraction
5
7

1
​

Answer 1

To simplify the expression \( 5^{-2} \times 5^{5} \), we can use the property of exponents which states that \( a^m \times a^n = a^{m+n} \).

Applying this property:

\[ 5^{-2} \times 5^{5} = 5^{-2 + 5} = 5^{3} \]

Now let's check the multiple choice options:

1. \(\frac{1}{5^{10}}\)
2. \(5^{3}\)
3. \(\frac{1}{5^{3}}\)
4. \(\frac{1}{5^{7}}\)

The equivalent expression we derived, \( 5^{3} \), matches option 2:

Answer: \( 5^{3} \)