Question

What is the following sum? 2 (RootIndex 3 StartRoot 16 x cubed y EndRoot) 4 (RootIndex 3 StartRoot 54 x Superscript 6 Baseline y Superscript 5 Baseline) 4 x (RootIndex 3 StartRoot 2 y EndRoot) 12 x squared y (RootIndex 3 StartRoot 2 y squared EndRoot) 8 x (RootIndex 3 StartRoot x y EndRoot) 12 x cubed y squared (RootIndex 3 StartRoot 6 y EndRoot) 16 x cubed y (RootIndex 3 StartRoot 2 y squared EndRoot) 48 x cubed y (RootIndex 3 StartRoot 2 y EndRoot).

Answer 1

Equivalent expressions are expressions that have the same value, and can be used interchangeably.

The result of the sum $2 (\sqrt[3]{16x^3y}) + 4 (\sqrt[3]{54x^6y^5})$ is $4x\sqrt[3]{2y} + 8x^2y\sqrt[3]{2y^2})$

The expression is given as:

$2 (\sqrt[3]{16x^3y}) + 4 (\sqrt[3]{54x^6y^5})$

Rewrite the expression as:

$2 (\sqrt[3]{16x^3y}) + 4 (\sqrt[3]{54x^6y^5}) = 2 (\sqrt[3]{2^4x^3y}) + 4 (\sqrt[3]{3^3 \times 2x^6y^5})$

Evaluate the roots

$2 (\sqrt[3]{16x^3y}) + 4 (\sqrt[3]{54x^6y^5}) = 2 (2x\sqrt[3]{2y}) + 4 (3x^2y\sqrt[3]{2y^2})$

Open the brackets

$2 (\sqrt[3]{16x^3y}) + 4 (\sqrt[3]{54x^6y^5}) = 4x\sqrt[3]{2y} + 12x^2y\sqrt[3]{2y^2})$

The above expression cannot be further simplified.

Hence, the result of the sum $2 (\sqrt[3]{16x^3y}) + 4 (\sqrt[3]{54x^6y^5})$ is $4x\sqrt[3]{2y} + 8x^2y\sqrt[3]{2y^2})$

Read more about equivalent expressions at:

brainly.com/question/2972832

Answer 2

The sum of the expression is $4 (\sqrt[3]{x^3y} +12x^2y(\sqrt[3]{ 2 y^2})$.

We have to determine, the sum of the given expression.

According to the question,

Expression; $2(\sqrt[3]{16x^3y} +4(\sqrt[3]{56x^6y^5})$

To determine the sum of the given expression following all the steps given below.

Rewrite the expression term in the form of their cubes,

$\rm = 2(\sqrt[3]{16x^3y} +4(\sqrt[3]{56x^6y^5})\\\\ = 2(\sqrt[3]{2^4x^3y} +4(\sqrt[3]{3^3 \times 2 \times x^6y^5})\\\\= 2\times 2(\sqrt[3]{x^3y} +4\times 3(\sqrt[3]{ 2 \times x^6y^5})\\\\= 4 (\sqrt[3]{x^3y} +12x^2y(\sqrt[3]{ 2 y^2})\\\\=4 (\sqrt[3]{x^3y} +12x^2y(\sqrt[3]{ 2 y^2})$

Hence, The sum of the expression is $4 (\sqrt[3]{x^3y} +12x^2y(\sqrt[3]{ 2 y^2})$.

For more details refer to the link given below.

brainly.com/question/21798224