Question

What is the cube root of 216x^9y^16

Answer 1

The cube root of
`\sqrt[3]{216x^9y^(16)} \,\,is\,\,6x^3y^(16/3)`

Explanation:

We need to find the cube root of 216x^9y^16

`\sqrt[3]{216x^9y^(16)} \\can\,\, be\,\, written\,\, as\,\,\\=\sqrt[3]{216} \sqrt[3]{x^9} \sqrt[3]{x^(16)} \\=\sqrt[3]{6x6x6} \sqrt[3]{x^9} \sqrt[3]{x^(16)} \\we\,\, know\,\,\sqrt[3]{x} = x^(1/3)\\= (6^3)^(1/3) (x^9)^(1/3)(y^(16))^(1/3)\\= 6x^3y^(16/3)`

So, the cube root of
`\sqrt[3]{216x^9y^(16)} \,\,is\,\,6x^3y^(16/3)`

Answer 2

`{ {6}{x}^(3) {y}^{ (16)/(3) } }`

EXPLANATION

We want to find the cube root of

`216 {x}^(9) {y}^(16)`

This is the same as:

`\sqrt[3]{216 {x}^(9) {y}^(16) }`

We rewrite as radical exponent to get;

`{(216 {x}^(9) {y}^(16) )}^{ (1)/(3) }`

This implies that;

`{( {6}^(3) {x}^(9) {y}^(16) )}^{ (1)/(3) }`

This simplifies to:

`{ {6}^{ (3)/(3) } {x}^{ (9)/(3) } {y}^{ (16)/(3) } }`

Hence the cube root is:

`{ {6}{x}^(3) {y}^{ (16)/(3) } }`