What is the simplest form of the following expression? \sqrt[3]{ (12x ^(2) )/(16y) }

Question

What is the simplest form of the following expression?


`\sqrt[3]{ (12x ^(2) )/(16y) }`

Answer 1

`\sqrt[3]{ (12x ^(2) )/(16y) } = \sqrt[3]{(3x ^(2) )/(4y) }`

Answer 2

The simplest form of the following expression is
`\sqrt[3]{(3x^2)/(4y)}`

Explanation:

The given expression is

`\sqrt[3]{(12x^2)/(16y)}`

Factor the numerator and denominator.

`\sqrt[3]{(3* 4* x^2)/(4* 4* y)}`

3 is common factor. Cancel out the common factor.

`\sqrt[3]{(3* x^2)/(4* y)}`

`\sqrt[3]{(3x^2)/(4y)}`

Therefore the simplest form of the following expression is
`\sqrt[3]{(3x^2)/(4y)}`.