Which of the following is an equivalent expression to 13−5 ⋅13−11 with only positive exponents, generated by applying the properties of exponents?(1 point)
Responses
12616
Start Fraction 1 over 26 superscript 16 baseline end fraction
11316
Start Fraction 1 over 13 superscript 16 baseline end fraction
1266
Start Fraction 1 over 26 superscript 6 baseline end fraction
1136
The equivalent expression is Start Fraction 1 over 13 superscript 16 baseline end fraction.
To simplify the expression 13−5 ⋅13−11, we can start by applying the product rule of exponents, which states that when multiplying two powers with the same base, we can add their exponents.
So, 13−5 ⋅13−11 can be written as 13(−5+−11).
Next, we apply the sum rule of exponents, which states that when adding two powers with the same base, we can add their exponents.
So, 13(−5+−11) simplifies to 13^(-16).
Therefore, the equivalent expression with only positive exponents is Start Fraction 1 over 13 superscript 16 baseline end fraction.
Therefore, the correct answer is: Start Fraction 1 over 13 superscript 16 baseline end fraction.