Question

Simplify completely: 12x11y · 1848062" y? 16O 6x^y? V6xO 6x"y? 6xO 216'ya

Answer 1

Given:

$\sqrt[]{12x^{11}y^6}.\sqrt[]{18y^8}$

To simplify this, we can follow the steps below

$\sqrt[]{12x^{11}y^6}.\sqrt[]{18y^8}=\sqrt[]{12\times18\times x^{11}\times y^6\times y^8}$

This can be simplified further

$\sqrt[]{216\times x^{11}\times y^{14}}$

Then we will obtain

$\sqrt[]{216\text{ }}\text{ x }\sqrt[]{x^{11}}\text{ x}\sqrt[]{y^{14}}$

=>

$6\sqrt[]{6}\times x^{\frac{11}{2}}\times y^{\frac{14}{2}}$

=>

$6\sqrt[]{6}\text{ }\times(x^{5+\frac{1}{2}})\times y^7$

=>

$6\sqrt[]{6}\text{ }\times x^5\times x^{\frac{1}{2}}\times y^7$

=>

$6\sqrt[]{6}\text{ }\times x^5\times\sqrt[]{x}\text{ }\times y^7$

=>

$6x^5y^7\sqrt[]{6x}$