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

1/26^16

1/26^6

1/13^6

1/13^16

Answer 1

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

Applying this property:

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

Now we need to convert \( 13^{-16} \) into a form with only positive exponents. This can be done using the property that \( a^{-n} = \frac{1}{a^n} \):

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

Among the choices provided, \( \frac{1}{13^{16}} \) is equivalent to:

1/13^16

So the answer is:

1/13^16