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)

Question

Responses

1/13^16
Start Fraction 1 over 13 superscript 16 baseline end fraction

1/13^6
Start Fraction 1 over 13 Superscript 6 baseline End Fraction

1/26^6
Start Fraction 1 over 26 superscript 6 baseline end fraction

1/26^16

Answer 1

To simplify \( 13^{-5} \cdot 13^{-11} \) using the properties of exponents, we apply the rule 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 only positive exponents, we recall that \( a^{-n} = \frac{1}{a^n} \): \[ 13^{-16} = \frac{1}{13^{16}} \]

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

So the correct answer is: \[ \text{1/13}^{{16}} \]