Question

What is the following product?

Answer 1

Answer: Last Option

`4x^5\sqrt[3]{3x}`

Explanation:

To make the product of these expressions you must use the property of multiplication of roots:

`\sqrt[n]{x^m}*\sqrt[n]{x^b} = \sqrt[n]{x^(m+b)}`

we also know that:

`\sqrt[3]{x^3} = x`

So

`\sqrt[3]{16x^7}*\sqrt[3]{12x^9}\\\\\sqrt[3]{16x^3x^3x}*\sqrt[3]{12(x^3)^3}\\\\x^2\sqrt[3]{16x}*x^3\sqrt[3]{12}\\\\x^5\sqrt[3]{16x*12}\\\\x^5\sqrt[3]{2^4x*2^2*3}\\\\x^5\sqrt[3]{2^6x*3}\\\\4x^5\sqrt[3]{3x}`