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

1/26⁶
1/13⁶
1/13¹⁶
1/26¹⁶

Answer 1

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

So, we have:

\[ 13^{-5} \cdot 13^{-11} = 13^{-5 + (-11)} = 13^{-16} \]

Now, to convert this to an expression with only positive exponents, we use the property that \( a^{-n} = \frac{1}{a^n} \):

\[ 13^{-16} = \frac{1}{13^{16}} \]

Now, looking at the answer choices you provided:

1. \( \frac{1}{26^6} \)
2. \( \frac{1}{13^6} \)
3. \( \frac{1}{13^{16}} \)
4. \( \frac{1}{26^{16}} \)

The equivalent expression to \( 13^{-5} \cdot 13^{-11} \) with only positive exponents is:

\[ \frac{1}{13^{16}} \]

So, the correct answer is \( \frac{1}{13^{16}} \).