Question

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 11316 Start Fraction 1 over 13 superscript 16 baseline end fraction 1136 Start Fraction 1 over 13 Superscript 6 baseline End Fraction 1266 Start Fraction 1 over 26 superscript 6 baseline end fraction 12616

Answer 1

To simplify the expression \( 13^{-5} \cdot 13^{-11} \) using the properties of exponents, we can apply the property that states \( a^m \cdot a^n = a^{m+n} \).

1. First, add the exponents:
\[
-5 + (-11) = -16.
\]
So, we have:
\[
13^{-5} \cdot 13^{-11} = 13^{-16}.
\]

2. Next, to express this with a positive exponent, we can use the property \( a^{-n} = \frac{1}{a^n} \):
\[
13^{-16} = \frac{1}{13^{16}}.
\]

Thus, the equivalent expression to \( 13^{-5} \cdot 13^{-11} \) with only positive exponents is:
\[
\frac{1}{13^{16}}.
\]

From the options provided, the correct choice is:
\[
\frac{1}{13^{16}}.
\]

There may be an error in your response options since \( \frac{1}{13^{16}} \) is what we found, and it resembles \( 11316 \) assuming it means \( \frac{1}{13^{16}} \). Please double-check the format. If those are codes and represent different numerical formats, you would need to clarify.