https://file.aiquickdraw.com/mathbot/file/1727823012409cuf8v5pv.jpg

The given question asks which radical expression is equivalent to \( y^{\frac{8}{3}} \).

To solve this, we can rewrite \( y^{\frac{8}{3}} \) as a radical expression. The general rule for converting exponents to radical form is:

\[
a^{\frac{m}{n}} = \sqrt[n]{a^m}
\]

Using this rule, \( y^{\frac{8}{3}} \) can be written as:

\[
y^{\frac{8}{3}} = \sqrt[3]{y^8}
\]

This matches option **D**, which represents \( \sqrt[3]{y^8} \), or equivalently, the cube root of \( y^8 \).

Thus, the correct answer is **D**.

Would you like more details on this or have any other questions?

Here are 5 related questions for further exploration:
1. How do you convert a fractional exponent into a radical expression?
2. What is the difference between a cube root and a square root?
3. How can you simplify \( y^{\frac{8}{3}} \) further?
4. What is the general rule for converting exponents into radical forms?
5. How can radical expressions be used in solving equations?

**Tip**: When dealing with fractional exponents, the numerator indicates the power, and the denominator indicates the root.

Which radical expression is equivalent to y^{8/3}?

Learn how to convert the expression y^{8/3} into a radical form. The problem focuses on exponent-to-radical conversion, demonstrating how fractional exponents can be rewritten as roots. Suitable for Grades 9-11 students learning Algebra.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation