Which of the following is equivalent to 6^−2?(1 point)
Responses
A. 1/6^2
B. 1/36
C. 1/12
D. 36
whcih one is it?
The correct answer is B. 1/36.
Which of the following is developed to be equivalent to 1/8^5?(1 point)
The expression equivalent to 1/8^5 is 8^-5.
Question
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)
To simplify the expression 13^-5 ⋅ 13^-11 with only positive exponents, we can apply the property of exponents that states when multiplying two numbers with the same base, we add the exponents.
So, 13^-5 ⋅ 13^-11 can be rewritten as 13^(-5 + -11).
Simplifying the exponent, we get 13^-16.
Therefore, an equivalent expression to 13^-5 ⋅ 13^-11 with only positive exponents is 1/13^16.
So, the correct answer is: A. 1/13^16.
Which of the following is an equivalent expression to 14^−7 / 9^−13 with only positive exponents, generated by applying the Property of Negative Integer Exponents?(1 point)
To simplify the expression 14^-7 / 9^-13 with only positive exponents, we can use the Property of Negative Integer Exponents, which states that a^(-n) is equal to 1 / a^n.
Applying this property to our expression, we have:
14^-7 / 9^-13 = 1 / 14^7 * 1 / 9^(-13)
Since multiplying two numbers with the same base is equivalent to adding their exponents, we can rewrite the expression as:
1 / (14^7 * 9^(-13))
Now, to make the exponent of 9 positive, we can apply the property a^(-n) = 1 / a^n once again:
1 / (14^7 * 1 / 9^13) = 1 / (14^7 * 1 / 9^13)
Simplifying further, we have:
1 / (1 / (14^7 * 9^13)) = 14^7 * 9^13
Therefore, an equivalent expression to 14^-7 / 9^-13 with only positive exponents is 14^7 * 9^13.
So, the correct answer is: C. 14^7 * 9^13.
Which of the following is an equivalent expression to 7^3/25^−4 with only positive exponents, generated by applying the Property of Negative Integer Exponents?(1 point
To simplify the expression 7^3/25^-4 with only positive exponents, we can use the Property of Negative Integer Exponents, which states that a^(-n) is equal to 1 / a^n.
Applying this property to our expression, we have:
7^3 / 25^-4 = 7^3 / (1 / 25^4)
Now, to make the exponent of 25 positive, we can apply the property a^(-n) = 1 / a^n:
7^3 / (1 / 25^4) = 7^3 * 25^4
Therefore, an equivalent expression to 7^3/25^-4 with only positive exponents is 7^3 * 25^4.
So, the correct answer is: D. 7^3 * 25^4.
ty all right except 4 which is 9^13/14^7
I apologize for the confusion. You are absolutely right. The correct equivalent expression to 14^-7 / 9^-13, with only positive exponents, generated by applying the Property of Negative Integer Exponents is 9^13 / 14^7.
Thank you for catching that mistake.