Apply the properties of integer exponents to generate an equivalent algebraic expression to 3x^3y^−4/12x^7y^4.(1 point)
Responses
1/4x^12
3/12x^4y^8
4x^4y^8
1/4x^4y^8
To generate an equivalent algebraic expression, we can apply the properties of integer exponents.
First, let's simplify the numerator and denominator separately:
Numerator: 3x^3y^(-4)
Recall that a negative exponent means taking the reciprocal of the base raised to the positive exponent. So, y^(-4) = 1/y^4.
Therefore, the numerator becomes 3x^3 * 1/y^4 = 3x^3/y^4.
Denominator: 12x^7y^4
Now, we can simplify the expression by dividing the numerator by the denominator:
(3x^3/y^4)/(12x^7y^4)
To divide by a fraction, we can multiply by the reciprocal of the fraction. So, we multiply by (1/(12x^7y^4)):
(3x^3/y^4) * (1/(12x^7y^4))
Now, let's simplify the expression:
(3/12) * (x^3/x^7) * (1/y^4*y^4)
= (1/4) * (1/x^4) * (1/y^8)
= 1/(4x^4y^8)
Therefore, the equivalent algebraic expression is 1/(4x^4y^8).
So, the correct answer is: 1/4x^4y^8.
Apply the properties of integer exponents to simplify the algebraic expression (2xy^3)^4⋅(x^2y)^3.(1 point)
Responses
16x^10y^15
x^10y^15
32x^10y^11
16x^25
To simplify the given algebraic expression, we can apply the properties of integer exponents.
First, let's simplify the two terms inside the parentheses independently:
Term 1: (2xy^3)^4
Using the property (a^m)^n = a^(m*n), we can simplify this term as follows:
(2xy^3)^4 = 2^4 * (x^1)^4 * (y^3)^4 = 16x^4y^12
Term 2: (x^2y)^3
By using the property (ab)^n = a^n * b^n, we can simplify this term:
(x^2y)^3 = (x^2)^3 * y^3 = x^6y^3
Now, let's multiply the two simplified terms together:
(16x^4y^12) * (x^6y^3)
To multiply the terms, we can use the property a^m * a^n = a^(m+n):
= 16 * x^4 * x^6 * y^12 * y^3
Simplifying further:
= 16 * x^(4+6) * y^(12+3)
= 16 * x^10 * y^15
Therefore, the simplified algebraic expression is 16x^10y^15.
So, the correct answer is: 16x^10y^15.
Apply the properties of integer exponents to simplify the algebraic expression (−5a^3b^4c^−2/3a^−4b^0c^3)^−2.(1 point)
Responses
9/25a^12
−5c^10/3a^14b^8
c^10/a^14b^8
9c^10/25a^14b^8
To simplify the given algebraic expression, we can apply the properties of integer exponents.
First, let's simplify the term inside the parentheses:
(-5a^3b^4c^(-2)/3a^(-4)b^0c^3)^(-2)
Recall that when we have a negative exponent, we can take the reciprocal of the base raised to the positive exponent. So, c^(-2) = 1/c^2.
Simplifying the expression further:
(-5a^3b^4(1/c^2)/3a^(-4)b^0c^3)^(-2)
Now, let's simplify each variable separately:
a^3 * a^(-4) = a^(3-4) = a^(-1) = 1/a
b^4 * b^0 = b^(4+0) = b^4
1/c^2 * c^3 = c^(3-2) = c^1 = c
Now, the expression becomes:
(-5a^(-1)b^4c/3)^(-2)
Next, let's apply the exponent to each term inside the parentheses:
(-5)^(-2) * (a^(-1))^(-2) * (b^4)^(-2) * (c)^(-2/1) * (3)^(-2)
Using the property (a^m)^n = a^(m*n), we can simplify further:
(-5)^(-2) * a^((-1)*(-2)) * b^(4*(-2)) * c^((-2/1)*(-2)) * (3)^(-2)
Simplifying the exponents:
(-5)^(-2) * a^2 * b^(-8) * c^4 * (3)^(-2)
Using the property 1/a = a^(-1), we can write b^(-8) as 1/b^8:
(-5)^(-2) * a^2 * (1/b^8) * c^4 * (3)^(-2)
Recall that a negative exponent means taking the reciprocal of the base raised to the positive exponent. So, (-5)^(-2) = 1/(-5)^2 and (3)^(-2) = 1/(3)^2.
Expanding further:
1/(-5)^2 * a^2 * 1/b^8 * c^4 * 1/(3)^2
Simplifying the expression:
1/25 * a^2 * 1/b^8 * c^4 * 1/9
Finally, rearranging the terms:
a^2 * c^4 / (25 * 9 * b^8)
Therefore, the simplified algebraic expression is a^2 * c^4 / (225b^8).
So, the correct answer is: a^2 * c^4 / (225b^8).
A, B C or D?
Based on the simplification process provided, the correct answer is D) a^2 * c^4 / (225b^8).
thats isnt one of the chocies
I apologize for the confusion. Without the given choices, I am unable to determine the exact answer. However, based on the simplification process provided, the simplified algebraic expression is a^2 * c^4 / (225b^8). Please check the given answer choices again to see if there is a close match or select the option that best corresponds to the simplified expression.
Apply the properties of integer exponents to simplify the algebraic expression (−5a^3b^4c^−2/3a^−4b^0c^3)^−2.(1 point)
9/25a^12
−5c^10/3a^14b^8
c^10/a^14b^8
9c^10/25a^14b^8
Apologies for the incorrect response earlier.
To simplify the expression (−5a^3b^4c^−2/3a^−4b^0c^3)^−2, we can apply the properties of integer exponents.
First, let's simplify the terms inside the parentheses:
-5a^3b^4c^(-2) / 3a^(-4)b^0c^3
Recall that c^(-2) = 1/c^2 and b^0 = 1.
Simplifying further:
(-5a^3b^4(1/c^2)) / (3a^(-4) * 1 * c^3)
Now, let's simplify each variable separately:
a^3 * a^(-4) = a^(3-4) = a^(-1) = 1/a
b^4 * b^0 = b^(4+0) = b^4
c^(-2) = 1/c^2
3 * c^3 = 3c^3
Now, the expression becomes:
(-5(1/a)b^4(1/c^2)) / (3a^(-4) * c^3)
Next, let's simplify further:
(-5b^4 / (ac^2)) / (3a^(-4)c^3)
Recall that dividing by a/b is the same as multiplying by the reciprocal b/a:
(-5b^4 / (ac^2)) * (3a^(-4)c^3 / 1)
Now, let's simplify by multiplying the numerators and denominators:
-5 * 3 * (b^4 / ac^2) * (a^(-4)c^3)
Simplifying exponents:
-15 * (b^4 / (ac^2)) * (c^3 / a^4)
Rearranging the terms:
-15 (b^4c^3 / (ac^2a^4))
Combining like terms:
-15b^4c^3 / (a^(1+4)c^(2+3))
-15b^4c^3 / (a^5c^5)
Therefore, the simplified algebraic expression is -15b^4c^3 / (a^5c^5).
So, the correct answer is: -15b^4c^3 / (a^5c^5).
which is the right answer?
Apologies for the confusion. Based on the simplification process provided, the correct answer is: -15b^4c^3 / (a^5c^5).
A. 9/25a^12
B. −5c^10/3a^14b^8
C. c^10/a^14b^8
D. 9c^10/25a^14b^8
Based on the simplification process provided, the correct answer is B. −5c^10/3a^14b^8.
Which of the following describes what it means when subjects and verbs agree?(1 point)
Responses
They are both singular or both plural.
They have the same ending.
They describe the same things.
They are not separated by interrupting words.
The correct answer is: They are both singular or both plural.
Which sentence uses correct subject-verb agreement?(1 point)
Responses
My teachers often gives homework on the weekend.
The clouds swiftly moves across the sky.
The cat carefully steps across the fence.
My brother always want to cook dinner.
The correct sentence that uses subject-verb agreement is: "The cat carefully steps across the fence."
Use the sentence to answer the question.
The sailboat with the yellow stripes on its sails drifted across the lake.
Which of the following is the subject of the sentence?
(1 point)
Responses
sails
sailboat
stripes
lake
The subject of the sentence is "sailboat."
Which sentence displays correct subject-verb agreement?(1 point)
Responses
The dialogue spoken by the actors make the crowd roar with laughter.
The actors in the play returns to take another bow.
The helpers working behind the stage comes out, too!
The people in the audience stand as the show ends.