Equivalent expressions are expressions that have the same value, and can be used interchangeably.
The result of the sum
is ![4x\sqrt[3]{2y} + 8x^2y\sqrt[3]{2y^2})](https://tex.z-dn.net/?f=4x%5Csqrt%5B3%5D%7B2y%7D%20%20%2B%208x%5E2y%5Csqrt%5B3%5D%7B2y%5E2%7D%29)
The expression is given as:
![2 (\sqrt[3]{16x^3y}) + 4 (\sqrt[3]{54x^6y^5})](https://tex.z-dn.net/?f=2%20%28%5Csqrt%5B3%5D%7B16x%5E3y%7D%29%20%20%2B%204%20%28%5Csqrt%5B3%5D%7B54x%5E6y%5E5%7D%29)
Rewrite the expression as:
![2 (\sqrt[3]{16x^3y}) + 4 (\sqrt[3]{54x^6y^5}) = 2 (\sqrt[3]{2^4x^3y}) + 4 (\sqrt[3]{3^3 \times 2x^6y^5})](https://tex.z-dn.net/?f=2%20%28%5Csqrt%5B3%5D%7B16x%5E3y%7D%29%20%20%2B%204%20%28%5Csqrt%5B3%5D%7B54x%5E6y%5E5%7D%29%20%3D%202%20%28%5Csqrt%5B3%5D%7B2%5E4x%5E3y%7D%29%20%20%2B%204%20%28%5Csqrt%5B3%5D%7B3%5E3%20%5Ctimes%202x%5E6y%5E5%7D%29)
Evaluate the roots
![2 (\sqrt[3]{16x^3y}) + 4 (\sqrt[3]{54x^6y^5}) = 2 (2x\sqrt[3]{2y}) + 4 (3x^2y\sqrt[3]{2y^2})](https://tex.z-dn.net/?f=2%20%28%5Csqrt%5B3%5D%7B16x%5E3y%7D%29%20%20%2B%204%20%28%5Csqrt%5B3%5D%7B54x%5E6y%5E5%7D%29%20%3D%202%20%282x%5Csqrt%5B3%5D%7B2y%7D%29%20%20%2B%204%20%283x%5E2y%5Csqrt%5B3%5D%7B2y%5E2%7D%29)
Open the brackets
![2 (\sqrt[3]{16x^3y}) + 4 (\sqrt[3]{54x^6y^5}) = 4x\sqrt[3]{2y} + 12x^2y\sqrt[3]{2y^2})](https://tex.z-dn.net/?f=2%20%28%5Csqrt%5B3%5D%7B16x%5E3y%7D%29%20%20%2B%204%20%28%5Csqrt%5B3%5D%7B54x%5E6y%5E5%7D%29%20%3D%204x%5Csqrt%5B3%5D%7B2y%7D%20%20%2B%2012x%5E2y%5Csqrt%5B3%5D%7B2y%5E2%7D%29)
The above expression cannot be further simplified.
Hence, the result of the sum
is ![4x\sqrt[3]{2y} + 8x^2y\sqrt[3]{2y^2})](https://tex.z-dn.net/?f=4x%5Csqrt%5B3%5D%7B2y%7D%20%20%2B%208x%5E2y%5Csqrt%5B3%5D%7B2y%5E2%7D%29)
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brainly.com/question/2972832
The value of x in (1/6)/2 = x/3 is 1
<h3>How to solve for x?</h3>
The equation is given as
(1/6)/2 = x/3
Cross multiply in the above equation
x * 2 = (1/6) * 3
This gives
x * 2 = 1/2
Cross multiply
x = 2 * 1/2
This gives
x = 1
Hence, the value of x in (1/6)/2 = x/3 is 1
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As x heads off to positive infinity, f(x) will do the same. This means f(x) grows without bound in the positive x direction.
However, in the other direction, as x goes to negative infinity things are a bit different. Instead of going off to infinity, f(x) will approach y = 0. It will never touch or cross this horizontal line. It will only get closer and closer. Think of it as an electric fence you can't touch.
So there is only one horizontal asymptote and it is the horizontal line y = 0. This is the horizontal line that overlaps the x axis.
No, some of the terms changed signs, the correct option is C.
Given
Maggie used the commutative property to write;

<h3>Commutative property</h3>
The commutative property of addition states that the sum of any two numbers remains the same even when the position of the numbers is interchanged.
Then,
She did not apply the commutative property correctly because she changed the signs of 4/5 and 8 and in consequence, the result will not be the same.
A, B and C, for a commutative property
(A+B)+C = C+(A+B)
4/5 + 6.9y - 8 as the equivalent expression of:
6.9y + 8 - 4/5
Hence, No, some of the terms changed signs.
To know more about commutative property click the link given below.
brainly.com/question/778086
Answer:
M
Step-by-step explanation: