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

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

Start Fraction 1 over 13 Superscript 6 baseline End Fraction

Start Fraction 1 over 13 superscript 16 baseline end fraction

Start Fraction 1 over 26 superscript 16 baseline end fraction

Start Fraction 1 over 26 superscript 6 baseline end fraction

Answer 1

The correct equivalent expression with positive exponents is:

Start Fraction 1 over 26 Superscript 6 baseline End Fraction

Answer 2

To find an equivalent expression with only positive exponents, we can rewrite 13-5 ⋅13-11 using the properties of exponents.

First, let's simplify 13-5 and 13-11 separately:

13-5 = 1/13^5
13-11 = 1/13^11

Now, let's multiply these two expressions:

(1/13^5) ⋅ (1/13^11)

To simplify this further, we can add the exponents when we multiply:

1/13^(5 + 11) = 1/13^16

Therefore, the equivalent expression with only positive exponents is Start Fraction 1 over 13 raised to the power of 16 end fraction.

So the answer is: Start Fraction 1 over 13 superscript 16 baseline end fraction.