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\13^16

1\13^6

1\26^6

1\26^16

1 answer

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

Therefore, 13^(-5) ⋅ 13^(-11) is equivalent to:
1 / (13^5) ⋅ 1 / (13^11)

Simplifying this expression, we can use the property of multiplying fractions by multiplying the numerators and the denominators separately:

1 / (13^5) ⋅ 1 / (13^11) = (1 ⋅ 1) / (13^5 ⋅ 13^11)

Using the property that a^m ⋅ a^n = a^(m+n), we can simplify the expression further:

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

Therefore, the equivalent expression with only positive exponents is 1/13^16.

The correct answer is 1\13^16.