Use the quotient rule to simplify.
$\sqrt[3]{\frac{t}{8}}$

• A. $\frac{\sqrt{t}}{2}$
• B. $\frac{t}{2}$
• C. $\frac{\sqrt{t}}{8}$
• D. $\frac{{}^3\sqrt{t}}{2}$

Answer: (D)

Verified step by step guidance

1. Identify the expression to simplify: the cube root of (t divided by 8), which is written as \(\sqrt[3]{\frac{t}{8}}\).
2. Recall the quotient rule for radicals: \(\sqrt[n]{\frac{a}{b}} = \frac{\sqrt[n]{a}}{\sqrt[n]{b}}\). Apply this rule to separate the cube root of the fraction into a fraction of cube roots: \(\frac{\sqrt[3]{t}}{\sqrt[3]{8}}\).
3. Simplify the denominator \(\sqrt[3]{8}\). Since 8 is a perfect cube (\$8 = 2^3\(), \)\sqrt[3]{8} = 2$.
4. Rewrite the expression as \(\frac{\sqrt[3]{t}}{2}\) after simplifying the denominator.
5. The expression is now simplified using the quotient rule for radicals: \(\frac{\sqrt[3]{t}}{2}\).