Which of the following is an equivalent expression to 5^9⋅5^−13 with only positive exponents that has been generated by applying the Properties of Integer Exponents?(1 point)
Responses
1/5^4
5^4
5^9/5^−13
1/625
To simplify the expression 5^9 * 5^(-13) and obtain an equivalent expression with only positive exponents, we can apply the property of exponents that states: a^m * a^n = a^(m+n).
In this case, we have 5^9 * 5^(-13). Using the property mentioned above, we can add the exponents together:
9 + (-13) = -4.
Therefore, an equivalent expression with only positive exponents can be written as 5^(-4). Rewriting it with positive exponents, we get:
1/5^4.
So the correct answer is 1/5^4.
Which property of exponents was used to generate the equivalent expression 3^14 from 3^5/3^−9?(1 point)
Responses
only the Property of Negative Exponents
the Property of Negative Exponents and the Product Rule of Exponents
only the Power Rule of Exponents
only the Product Rule of Exponents
The property of exponents that was used to generate the equivalent expression 3^14 from 3^5/3^(-9) is the Product Rule of Exponents.
The Product Rule of Exponents states that when dividing two exponential expressions with the same base, you subtract the exponents. In this case, we have 3^5/3^(-9), and when we divide these two expressions, we subtract the exponents:
3^5 / 3^(-9) = 3^(5-(-9)) = 3^(5+9) = 3^14.
So, the correct answer is the Product Rule of Exponents.
Which of the following is an equivalent expression to 15^0 ⋅ 7^−2 (−4)^−3 with only positive exponents that has been generated by applying the Properties of Integer Exponents?(1 point)
Responses
(−4)^3/7^2
1/7^2 ⋅ (−4)^−3
4^3/7^2
7^2/(−4)^3
To simplify the expression 15^0 * 7^(-2) * (-4)^(-3) and obtain an equivalent expression with only positive exponents, we can apply the property of exponents that states:
a^0 = 1 for any nonzero value of a.
In this case, 15^0 = 1, so the expression can be simplified to:
1 * 7^(-2) * (-4)^(-3)
Next, we can apply the property of exponents that states:
a^(-n) = 1/a^n.
Using this property, we can rewrite 7^(-2) as 1/7^2 and (-4)^(-3) as 1/(-4)^3:
1 * 1/7^2 * 1/(-4)^3
Simplifying further, we get:
1/7^2 * 1/(-64)
To obtain an equivalent expression with positive exponents, we can rewrite the expression as:
1/7^2 * (-1/64)
Therefore, the correct answer is 1/7^2 * (-1/64).
not one of the responses idiot
I apologize for the inappropriate response. I'm sorry for the mistake.
To simplify the expression 15^0 * 7^(-2) * (-4)^(-3) and obtain an equivalent expression with only positive exponents, we can apply the property of exponents that states:
a^0 = 1 for any nonzero value of a.
In this case, 15^0 equals 1, so the expression can be simplified to:
1 * 7^(-2) * (-4)^(-3)
Next, we can apply the property of exponents that states:
a^(-n) = 1/a^n.
Using this property, we can rewrite 7^(-2) as 1/7^2 and (-4)^(-3) as 1/(-4)^3:
1 * 1/7^2 * 1/(-4)^3
Simplifying further, we get:
1/7^2 * 1/(-64)
To obtain an equivalent expression with positive exponents, we can rewrite the expression as:
1/7^2 * (-1/64)
Therefore, the correct answer is 1/7^2 * (-1/64). I apologize for my previous incorrect response.
Question: Do you see that answer you just provided as one of the answer choices?
I apologize for the confusion. I made an error in my previous response. After re-evaluating the expression, the correct answer choice that is equivalent to 15^0 * 7^(-2) * (-4)^(-3) and has only positive exponents is:
1/7^2 * (−4)^3
Thank you for bringing this to my attention, and I apologize for any inconvenience caused.
Which of the following is the equivalent expression to (15^−3 ⋅ 4^7)^0 / 4^−3 that has been generated by applying the Properties of Integer Exponents?(1 point)
Responses
60 / 4^−3
1⋅4^−3
1/64
64