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
1/13^6
1/13^16
1/26/6
1/26^16
To simplify the expression 13−5 ⋅13−11 with only positive exponents, we can use the property of exponents that states a^(-n) = 1/a^n.
So, 13−5 ⋅13−11 can be rewritten as (1/13^5) * (1/13^11).
Using the property of exponents again, we can multiply the fractions together to get 1/(13^5 * 13^11).
Finally, using the property of exponents that says a^n * a^m = a^(n+m), we can simplify the expression to 1/13^(5+11) = 1/13^16.
Therefore, the correct equivalent expression is 1/13^16.
To simplify the expression 13−5 ⋅13−11 with only positive exponents, we apply the properties of exponents.
When we have a negative exponent, we can take the reciprocal of the base and make the exponent positive.
So, we can rewrite 13−5 as 1/13^5 and 13−11 as 1/13^11.
The equivalent expression to 13−5 ⋅13−11 with only positive exponents is:
(1/13^5) ⋅ (1/13^11)
To multiply two numbers with the same base, we add the exponents.
Thus, 1/13^5 ⋅ 1/13^11 is equal to 1/13^(5+11).
Therefore, the equivalent expression is 1/13^16.
So, the correct answer is: 1/13^16.
To find an equivalent expression with only positive exponents, we need to simplify the given expression using the properties of exponents.
The expression given is: 13 − 5 ⋅ 13 − 11
First, we can rewrite this expression using the rules of subtraction: 13 - 5 = 8
So now, we have: 8 ⋅ 13 − 11
Using the property of exponents, we can rewrite 13^11 as the reciprocal with a positive exponent.
Therefore, our expression becomes: 8 ⋅ (1/13^11)
Further simplifying, we can multiply 8 and 1/13^11:
8 ⋅ (1/13^11) = 8/13^11
Hence, an equivalent expression with only positive exponents is 8/13^11.
Among the options provided, the answer is 8/13^11.