Question

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Answer 1

`\large\boxed{8x^3y^4\sqrt[3]{xy}}`

Explanation:

`\sqrt[3]{125x^(10)y^(13)}+\sqrt[3]{27x^(10)y^(13)}\qquad\text{use}\ \sqrt[n]{ab}=\sqrt[n]{a}\cdot\sqrt[n]{b}\\\\=\sqrt[3]{125}\cdot\sqrt[3]{x^(10)y^(13)}+\sqrt[3]{27}\cdot\sqrt[3]{x^(10)y^(13)}\\\\=5\sqrt[3]{x^(10)y^(13)}+3\sqrt[3]{x^(10)y^(13)}\\\\=8\sqrt[3]{x^(10)y^(13)}\\\\=8\sqrt[3]{x^(3+3+3+1)y^(3+3+3+3+1)}\qquad\text{use}\ a^na^m=a^(n+m)\\\\=8\sqrt[3]{x^3x^3x^3xy^3y^3y^3y}\qquad\text{use}\ \sqrt[n]{ab}=\sqrt[n]{a}\cdot\sqrt[n]{b}`

`=8\sqrt[3]{x^3}\cdot\sqrt[3]{x^3}\cdot\sqrt[3]{x^3}\cdot\sqrt[3]{y^3}\cdot\sqrt[3]{y^3}\cdot\sqrt[3]{y^3}\cdot\sqrt[3]{y^3}\cdot\sqrt[3]{xy}\qquad\text{use}\ \sqrt[n]{a^n}=a\\\\=8xxxyyyy\sqrt[3]{xy}\\\\=8x^3y^4\sqrt[3]{xy}`

Answer 2

∛125x^10y^13 + ∛27x^10y^13

= 5x^3y^4 ∛xy + 3x^3y^4 ∛xy

= 8x^3y^4 ∛xy

Answer is A. 8x^3y^4 ∛xy