Question

Write an equivalent expression for the 4th root of 324m^12 * the cubed root of 64k^9. Need help!

Answer 1

Answer:

The equivalent expression to the givan expression is

$\sqrt[4]{324m^{12}}\times\sqrt[3]{64k^9}=12\sqrt[4]{4}m^3k^3$

Step-by-step explanation:

Given expression is 4th root of 324m^12 * the cubed root of 64k^9

The given expression can be written as

$\sqrt[4]{324m^{12}}\times\sqrt[3]{64k^9}$

To find the equivalent expression to the given expression :

$\sqrt[4]{324m^{12}}\times\sqrt[3]{64k^9}$

$=\sqrt[4]{81\times 4m^{12}}\times\sqrt[3]{16\times 4k^9}$

$=\sqrt[4]{3\times 3\times 3\times 3\times 4m^{12}}\times\sqrt[3]{4\times 4\times 4k^9}$

$=\sqrt[4]{3\times 3\times 3\times 3\times 4m^{12}}\times\sqrt[3]{4\times 4\times 4k^9}$

$=(3\times \sqrt[4]{m^{12}})\times (4\times \sqrt[3]{k^9})$

$=(3\times \sqrt[4]{4m^{12}})\times (4\times \sqrt[3]{k^9})$

$=(3\times \sqrt[4]{4}\times (m^{12})^{\frac{1}{4}})\times (4\times {(k^9)^{\frac{1}{3}})$

$=(3\sqrt[4]{4}\times m^{\frac{12}{4}})\times (4\times k^{\frac{9}{3}})$

$=(3\sqrt[4]{4}\times m^3)\times (4\times k^3)$

$=3\sqrt[4]{4}m^3.4k^3$

$=12\sqrt[4]{4}m^3k^3$

$\sqrt[4]{324m^{12}}\times\sqrt[3]{64k^9}=12\sqrt[4]{4}m^3k^3$

Therefore the equivalent expression to the given expression is

$\sqrt[4]{324m^{12}}\times\sqrt[3]{64k^9}=12\sqrt[4]{4}m^3k^3$