Question

What is the following sum? ^3√125x^10y^13+^3√27x^10y^13

Answer 1

8x^3y^4(3 sqrt xy) LETTER A :)

Answer 2

Answer:

The sum of given expression $\sqrt[3]{125}x^{10}y^{13}+\sqrt[3]{27}x^{10}y^{13}$ is  $8x^{10}y^{13}$

Step-by-step explanation:

 Given : expression $\sqrt[3]{125}x^{10}y^{13}+\sqrt[3]{27}x^{10}y^{13}$

We have find the sum of given expression $\sqrt[3]{125}x^{10}y^{13}+\sqrt[3]{27}x^{10}y^{13}$

Consider the given expression $\sqrt[3]{125}x^{10}y^{13}+\sqrt[3]{27}x^{10}y^{13}$

$\sqrt[3]{125}=\sqrt[3]{5\times 5 \times 5}=\sqrt[3]{5^3}$

Apply radical rule, $\sqrt[n]{a^n}=a$

we have, $\sqrt[3]{125}=\sqrt[3]{5^3}=5$

Also,  $\sqrt[3]{27}=\sqrt[3]{3\times 3 \times 3}= \sqrt[3]{3^3}$

Apply radical rule, $\sqrt[n]{a^n}=a$

we have, $\sqrt[3]{27}=\sqrt[3]{3^3}=3$

Thus, given expression becomes,

$\sqrt[3]{125}x^{10}y^{13}+\sqrt[3]{27}x^{10}y^{13}$

$\Rightarrow 5x^{10}y^{13}+3x^{10}y^{13}$

Simplify, we get,

$\Rightarrow 8x^{10}y^{13}$

Thus, the sum of given expression $\sqrt[3]{125}x^{10}y^{13}+\sqrt[3]{27}x^{10}y^{13}$ is  $8x^{10}y^{13}$