Which of the following is an equivalent expression to 13−superscript5 ⋅13− superscript11

Question

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

1266
Start Fraction 1 over 26 superscript 6 baseline end fraction

12616
Start Fraction 1 over 26 superscript 16 baseline end fraction

1/13 superscript6

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, to convert \( 13^{-16} \) 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, let's compare this result to the provided options.

None of the options you provided directly match \( \frac{1}{13^{16}} \), but we can simplify the choices. The first options with \( \frac{1}{13^{16}} \) would be the correct choice.

So the equivalent expression with only positive exponents is:

Start Fraction 1 over 13 superscript 16 baseline end fraction.