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
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.
To simplify the expression 13^-5 * 13^-11, we can use the property of exponents that states: when multiplying two numbers with the same base, we add their exponents. Therefore, the equivalent expression would be 13^(-5 + -11) = 13^-16.
To convert this to an expression with only positive exponents, we can use the property that states: a^(-n) = 1 / a^n. Applying this property to 13^-16 gives us 1 / 13^16.
Therefore, the correct answer is option 3: 1/13^16.
To simplify the expression 13^-5 * 13^-11, we can apply the property of exponents that states: a^m * a^n = a^(m + n), where "a" represents the base and "m" and "n" represent the exponents.
So, combining the exponents, we have 13^(-5 + -11). Adding the exponents gives us -16, so the expression simplifies to 13^-16.
Since we want the expression with only positive exponents, we can rewrite 13^-16 as 1/13^16.
Therefore, the answer is option 3: 1/13^16.