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. 1/26^6
2. 1/13^6
3. 1/13^16
4. 1/26^16

1 answer

To find an equivalent expression with only positive exponents, we can use the property of exponents that states: a^(-n) = 1/a^n.

Therefore, 13^-5 * 13^-11 can be rewritten as 1/13^5 * 1/13^11.

Using the rule of multiplication, we can add the exponents when multiplying the same base, so 1/13^5 * 1/13^11 becomes 1/13^(5+11) = 1/13^16.

Therefore, the answer is option 3. 1/13^16.