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
1/26^16
1/13^16
1/13^6
1/26^6
To find an equivalent expression with positive exponents, we can add the exponents together.
13^(-5) ⋅ 13^(-11) can be written as 13^(-5 + (-11)) = 13^(-16)
Therefore, the equivalent expression with positive exponents is 1/13^16
The correct answer is 1/13^16.
To simplify the expression 13^(-5) * 13^(-11) and rewrite it with only positive exponents, you can apply the property of exponents that states when multiplying two powers with the same base, you add their exponents.
So, let's simplify the expression step by step:
First, we apply the property of exponents:
13^(-5) * 13^(-11) = 13^(-5 + -11)
Next, we add the exponents:
13^(-5 + -11) = 13^(-16)
Finally, to rewrite it with only positive exponents, we can take the reciprocal of the expression:
1 / 13^16
Therefore, the equivalent expression with only positive exponents is 1/13^16.
So, the correct response is 1/13^16.
To find an equivalent expression with positive exponents, we can use the properties of exponents. In this case, we have the expression 13^(-5) * 13^(-11).
The property we can use is the product of powers property, which states that when multiplying two numbers with the same base, we can add their exponents.
So, applying this property, we have 13^(-5) * 13^(-11) = 13^(-5 + -11) = 13^(-16).
To make the exponent positive, we can take the reciprocal of the base raised to the positive exponent. Therefore, the equivalent expression is 1 / 13^16.
So, the correct response is 1/13^16.