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
1/13^6
1/26^6
1/13^16
To simplify the expression 13−^5 ⋅13−^11 with only positive exponents, you can use the property that states when you multiply two numbers with the same base, you add the exponents.
Therefore, 13−^5 ⋅13−^11 can be written as 13^(-5 + (-11)).
Simplifying the exponents inside the parenthesis, we get 13^(-16).
The expression 13^(-16) is equivalent to 1/13^16.
So, the correct answer is 1/13^16.
To simplify the expression with positive exponents, we can apply the properties of exponents.
First, let's simplify 13^(-5) by applying the rule of negative exponents:
13^(-5) = 1 / 13^5
Next, let's simplify 13^(-11) in the same way:
13^(-11) = 1 / 13^11
Now, let's substitute these values back into the original expression:
13^(-5) * 13^(-11) = (1 / 13^5) * (1 / 13^11)
When multiplying fractions, we can simply multiply the numerators together and the denominators together:
(1 / 13^5) * (1 / 13^11) = 1 / (13^5 * 13^11)
To simplify this further, we can add the exponents of 13:
13^5 * 13^11 = 13^(5 + 11) = 13^16
Therefore, the equivalent expression to 13^(-5) * 13^(-11) with only positive exponents is 1 / 13^16.
Hence, the correct answer is 1/13^16.
To simplify the expression 13−^5 ⋅13−^11, we can use the property of exponents that states a^m ⋅ a^n = a^(m+n).
Let's follow these steps to simplify the expression:
Step 1: Apply the property of exponents.
13−^5 ⋅13−^11 = 13^(-5-11)
Step 2: Perform the subtraction inside the exponent.
13^(-5-11) = 13^(-16)
Step 3: Use the property of exponents that states a^(-n) = 1/a^n.
13^(-16) = 1/13^16
Therefore, the expression 13−^5 ⋅13−^11 simplified to 1/13^16.
Among the given answer choices, 1/13^16 is the expression that is equivalent to 13−^5 ⋅13−^11 with only positive exponents.