Which of the following is an equivalent expression to 11−13⋅11−7

Question

with only positive exponents, generated by applying the properties of exponents?(1 point)
Responses

1116
Start Fraction 1 over 11 superscript 6 baseline end fraction

1226
Start Fraction 1 over 22 superscript 6 baseline end fraction

12220
Start Fraction 1 over 22 superscript 20 baseline end fraction

11120

Answer 1

To simplify the expression \( 11^{-13} \cdot 11^{-7} \) using the properties of exponents, we can apply the property that states \( a^m \cdot a^n = a^{m+n} \).

1. Combine the exponents: \[ 11^{-13} \cdot 11^{-7} = 11^{-13 + (-7)} = 11^{-20} \]

2. To express this with only positive exponents, we use the property \( a^{-n} = \frac{1}{a^n} \): \[ 11^{-20} = \frac{1}{11^{20}} \]

Now, we need to see if any of the provided options match this expression:

1. \( 11^{16} \) -> Not equivalent
2. \( \frac{1}{22^{6}} \) -> Not equivalent
3. \( \frac{1}{22^{20}} \) -> Not equivalent
4. \( 11^{120} \) -> Not equivalent

None of the responses match \( \frac{1}{11^{20}} \). There may be a misunderstanding in the options provided.

The correct equivalent expression with only positive exponents should be: \[ \frac{1}{11^{20}} \]

If you intended for "22" to be involved, please clarify, but based on the operations performed, the correct answer is not listed among your provided options.