enter the correct answer in the box. if (x\neq0), what is the sum of (4sqrt3{x^{10}}+5x^{3}sqrt3{8x}) in…
enter the correct answer in the box. if (x\neq0), what is the sum of (4sqrt3{x^{10}}+5x^{3}sqrt3{8x}) in simplest form?
Answer
Explanation:
Step1: Simplify the first term
Rewrite $\sqrt[3]{x^{10}}$ as $\sqrt[3]{x^{9}\cdot x}=x^{3}\sqrt[3]{x}$. So $4\sqrt[3]{x^{10}} = 4x^{3}\sqrt[3]{x}$.
Step2: Simplify the second term
Rewrite $\sqrt[3]{8x}$ as $\sqrt[3]{8}\cdot\sqrt[3]{x}=2\sqrt[3]{x}$. Then $5x^{3}\sqrt[3]{8x}=5x^{3}\cdot2\sqrt[3]{x}=10x^{3}\sqrt[3]{x}$.
Step3: Combine like - terms
Add the two simplified terms: $4x^{3}\sqrt[3]{x}+10x^{3}\sqrt[3]{x}=(4 + 10)x^{3}\sqrt[3]{x}=14x^{3}\sqrt[3]{x}$.
Answer:
$14x^{3}\sqrt[3]{x}$