Answer:
The sum of given expression [tex]\sqrt[3]{125}x^{10}y^{13}+\sqrt[3]{27}x^{10}y^{13}[/tex] is [tex]8x^{10}y^{13}[/tex]
Step-by-step explanation:
Given : expression [tex]\sqrt[3]{125}x^{10}y^{13}+\sqrt[3]{27}x^{10}y^{13}[/tex]
We have find the sum of given expression [tex]\sqrt[3]{125}x^{10}y^{13}+\sqrt[3]{27}x^{10}y^{13}[/tex]
Consider the given expression [tex]\sqrt[3]{125}x^{10}y^{13}+\sqrt[3]{27}x^{10}y^{13}[/tex]
[tex]\sqrt[3]{125}=\sqrt[3]{5\times 5 \times 5}=\sqrt[3]{5^3}[/tex]
Apply radical rule, [tex]\sqrt[n]{a^n}=a[/tex]
we have, [tex]\sqrt[3]{125}=\sqrt[3]{5^3}=5[/tex]
Also, [tex]\sqrt[3]{27}=\sqrt[3]{3\times 3 \times 3}= \sqrt[3]{3^3}[/tex]
Apply radical rule, [tex]\sqrt[n]{a^n}=a[/tex]
we have, [tex]\sqrt[3]{27}=\sqrt[3]{3^3}=3[/tex]
Thus, given expression becomes,
[tex]\sqrt[3]{125}x^{10}y^{13}+\sqrt[3]{27}x^{10}y^{13}[/tex]
[tex]\Rightarrow 5x^{10}y^{13}+3x^{10}y^{13}[/tex]
Simplify, we get,
[tex]\Rightarrow 8x^{10}y^{13}[/tex]
Thus, the sum of given expression [tex]\sqrt[3]{125}x^{10}y^{13}+\sqrt[3]{27}x^{10}y^{13}[/tex] is [tex]8x^{10}y^{13}[/tex]
