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)
1/26^16
1/26^6
1/13^16
1/13^6
To simplify the given expression, we can rewrite it using the exponent rule that states: a^m ÷ a^n = a^(m-n).
Applying this rule to the expression 13−5 ⋅13−11, we have:
13^(-5) ⋅ 13^(-11) = 13^(-5 - 11) = 13^(-16).
Since we want an expression with only positive exponents, we can rewrite 13^(-16) as 1/13^16.
Therefore, the equivalent expression is 1/13^16.
To rewrite the expression with only positive exponents, we can use the property of exponents that states a^(-n) = 1/(a^n).
So, 13−5 can be rewritten as 1/13^5, and 13−11 can be rewritten as 1/13^11.
Therefore, the expression 13−5 ⋅13−11 is equivalent to (1/13^5) ⋅ (1/13^11).
To simplify the expression, we can use the property of exponents that states a^m ⋅ a^n = a^(m+n).
So, (1/13^5) ⋅ (1/13^11) = 1/(13^5 ⋅ 13^11).
To combine the bases with the same exponent, we can use the property of exponents that states a^m ⋅ b^m = (a ⋅ b)^m.
So, 13^5 ⋅ 13^11 can be rewritten as (13 ⋅ 13)^5 ⋅ 13^11 = 169^5 ⋅ 13^11.
Finally, the expression is equivalent to 1/(169^5 ⋅ 13^11).
Therefore, the correct answer is 1/(169^5 ⋅ 13^11).