Which of the following is an equivalent expression to 13^-5 × 13^-11 with only positive Exponents, generated by only applying the properties of Exponents?

1/20^16
1/26^6
1/13^6
1/13^16
1/13^17

1 answer

To find an equivalent expression with positive exponents, we can apply the property of exponents that states when multiplying two numbers with the same base, we add the exponents.

Therefore, 13^-5 × 13^-11 can be rewritten as 13^(-5 + -11) = 13^-16.

To convert this to an expression with positive exponents, we can take the reciprocal of the base, which will change the sign of the exponent. Thus,

1/13^-16 = 1/13^16.

Therefore, the correct option is 1/13^16.