which expression is equivalent to $sqrt3{x^{10}}$?\n$sqrt3{3x^{3}+x}$\n$sqrt3{3x^{3}cdot x}$\n$sqrt3{x^{3}+x^…
which expression is equivalent to $sqrt3{x^{10}}$?\n$sqrt3{3x^{3}+x}$\n$sqrt3{3x^{3}cdot x}$\n$sqrt3{x^{3}+x^{3}+x^{3}+x}$\n$sqrt3{x^{9}cdot x}$
Answer
Explanation:
Step1: Use exponent - rule
We know that (a^{m + n}=a^{m}\cdot a^{n}). So, (x^{10}=x^{9 + 1}=x^{9}\cdot x^{1}).
Step2: Apply cube - root property
(\sqrt[3]{x^{10}}=\sqrt[3]{x^{9}\cdot x}) since (\sqrt[3]{ab}=\sqrt[3]{a}\cdot\sqrt[3]{b}) and (x^{9}=(x^{3})^{3}), (\sqrt[3]{x^{9}} = x^{3}).
Answer:
(\sqrt[3]{x^{9}\cdot x}) (the fourth option)