Question

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

Answer 1

ANSWER

${ {6}{x}^{3} {y}^{ \frac{16}{3} } }$

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;

${(216 {x}^{9} {y}^{16} )}^{ \frac{1}{3} }$

This implies that;

${( {6}^{3} {x}^{9} {y}^{16} )}^{ \frac{1}{3} }$

This simplifies to:

${ {6}^{ \frac{3}{3} } {x}^{ \frac{9}{3} } {y}^{ \frac{16}{3} } }$

Hence the cube root is:

${ {6}{x}^{3} {y}^{ \frac{16}{3} } }$

Answer 2

Answer:

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

Step-by-step 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 $\sqrt[3]{216x^9y^{16}} \,\,is\,\,6x^3y^{16/3}$