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
7^2(−4)^3
4^3/7^2
(−4)^3/7^2
1/7^2 ⋅ (−4)^−3
To convert the expression to have only positive exponents, we can use the property that states a^(-n) = 1/a^n.
Using this property, we can rewrite the expression as:
15^0 ⋅ 7^(-2) / (-4)^(-3) = 15^0 ⋅ 1/7^2 ⋅ 1/(-4)^3
Since any number raised to the power of 0 is equal to 1, we can simplify 15^0 as 1:
1 ⋅ 1/7^2 ⋅ 1/(-4)^3 = 1/7^2 ⋅ 1/(-4)^3
So, the equivalent expression with only positive exponents is 1/7^2 ⋅ (−4)^−3.
Therefore, the correct answer is option D: 1/7^2 ⋅ (−4)^−3.
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)
60/4^−3
1/64
1⋅4^−3
64
To simplify the expression, let's use the property that states (a^m)^n = a^(m*n).
Using this property, we can simplify the expression as:
(15^(-3) ⋅ 4^7)^0/4^(-3) = (15^(-3*0) ⋅ 4^(7*0)) / 4^(-3)
Any number raised to the power of zero is equal to 1, so our expression becomes:
(1 ⋅ 1) / 4^(-3) = 1 / 4^(-3)
Now, we can use the property that states a^(-n) = 1/a^n.
Applying this property, we can rewrite the expression as:
1 / 4^(-3) = 1 / 1/4^3 = 1 / 1/64 = 64
So, the equivalent expression to (15^(-3) ⋅ 4^7)^0/4^(-3) that has been generated by applying the Properties of Integer Exponents is 64.
Therefore, the correct answer is option D: 64.
Which of the following is an equivalent expression to (2^−3 ⋅ 9^3)^−4/2^9 ⋅ 9^−10 with only positive exponents, generated by applying the Properties of Integer Exponents?(1 point)
Responses
2^3 ⋅9^2
2^12⋅9^−12/2^9⋅9^−10
2^−7⋅9^−1/2^9⋅9^−10
2^3/9^2
To simplify the expression and have only positive exponents, we can use the property that states a^(-n) = 1/a^n.
Starting with the expression, let's rewrite it one step at a time:
(2^(-3) ⋅ 9^3)^(-4) / 2^9 ⋅ 9^(-10)
Since any number raised to the power of 0 is equal to 1, we can simplify the negative exponent expressions:
(1/(2^3 ⋅ 9^(-3)))^(-4) / 2^9 ⋅ (1/9^10)
To simplify further, we can apply the property that (a^m)^n = a^(m*n):
(1/(2^3) ⋅ 9^(-3))^(-4) / 2^9 ⋅ (1/9^10)
Simplifying the exponents:
(1/8 ⋅ 1/9^3)^(-4) / 2^9 ⋅ (1/9^10)
To simplify the expression inside the parentheses, we multiply the fractions:
(1/(8 ⋅ 9^3))^(-4) / 2^9 ⋅ (1/9^10)
Simplifying the exponents further:
(1/8 ⋅ 1/729)^(-4) / 2^9 ⋅ (1/9^10)
Finally, we can simplify the expression inside the parentheses:
(1/(8/729))^(-4) / 2^9 ⋅ (1/9^10)
To divide by a fraction, we can multiply by its reciprocal:
(1 ⋅ 729/8)^(-4) / 2^9 ⋅ (1/9^10)
Simplifying the fractions:
(729/8)^(-4) / 2^9 ⋅ (1/9^10)
To further simplify, we can apply the property a^(-n) = 1/a^n and make all exponents positive:
(8/729)^4 / 2^9 ⋅ (1/9^10)
Therefore, the equivalent expression to (2^(-3) ⋅ 9^3)^(-4) / 2^9 ⋅ 9^(-10) with only positive exponents is (8/729)^4 / 2^9 ⋅ (1/9^10).
So, the correct answer is option B: 2^12⋅9^−12/2^9⋅9^−10.
Which of the following describes a gerund and how it functions in a sentence?(1 point)
Responses
A gerund is a noun that functions as the subject of a sentence.
A gerund is a verb ending in -ing that functions as a noun in a sentence.
A gerund is a verb ending in -ing that functions as a verb in a sentence.
A gerund is a noun that functions as the direct object receiving the action in a sentence.
The correct answer is:
A gerund is a verb ending in -ing that functions as a noun in a sentence.
A gerund is a type of verb form that ends in -ing and functions as a noun in a sentence. It can act as the subject, object, or complement in a sentence. For example, in the sentence "Running is my favorite hobby," the word "running" is a gerund that functions as the subject of the sentence.
Which sentence includes a gerund?(1 point)
Swimming in the gulf is Finn's favorite summer activity.
Graham learned to dive at the community swimming pool.
Nash has been swimming since he was five years old.
While swimming at the beach, Harper found a starfish.
The sentence that includes a gerund is:
"Swimming in the gulf is Finn's favorite summer activity."
Use the sentence to answer the question
"Traveling offers the opportunity to meet new people and experience exciting cultures."
How is the gerund functioning?
(1 point)
It describes the action of the subject.
It modifies a noun in the sentence.
It is the subject of the sentence.
It receives the action of the verb.