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
1136
11316
12616
1266
To simplify the expression 13−5 ⋅13−11, we can apply the property of exponents that states a^m * a^n = a^(m+n). This means that we can add the exponents when multiplying the same base.
Therefore, 13−5 ⋅13−11 can be simplified as 13^(−5+−11), which equals 13^−16.
Since we want only positive exponents, we can use the property that states a^−n = 1/(a^n), where a is any non-zero number. So, 13^−16 can be rewritten as 1/(13^16).
Therefore, the equivalent expression with only positive exponents is 1/(13^16).
The correct answer is (1 point) 1266.
To simplify the expression 13−5 ⋅13−11 with only positive exponents, we can apply the property of exponents which states that multiplying two numbers with the same base will add the exponents.
Step 1: Rewrite 13−5 ⋅ 13−11 using positive exponents.
= 1/135 ⋅ 1/1311
Step 2: Simplify the expression.
= 1/195 ⋅ 1/1511
Therefore, the equivalent expression with positive exponents is 12616.