https://file.aiquickdraw.com/mathbot/file/1727442545631ofqtfd46.jpg

The problem asks to express the radical \(\sqrt[3]{4^5}\) in exponential form. Let's break this down step-by-step.

### Conversion from Radical to Exponent:
The general form for converting a root to an exponent is:
\[
\sqrt[n]{a^m} = a^{m/n}
\]
In this case, the expression is \(\sqrt[3]{4^5}\), which means:
\[
\sqrt[3]{4^5} = 4^{5/3}
\]

Now, looking at the provided options:

- **A.** \(4^{5/3}\) — This matches the result.
- **B.** \(4^{3/5}\) — This is incorrect.
- **C.** \(4^{2/5}\) — This is incorrect.
- **D.** \(4^{3/4}\) — This is incorrect.

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

Would you like further clarification on the concept? Here are five related questions you can consider:

1. How do you convert any radical into its exponent form?
2. Can you simplify the expression \(\sqrt[4]{16^3}\) into an exponent?
3. What happens if you have fractional exponents with negative bases?
4. What is the rule for multiplying numbers with fractional exponents?
5. How do you handle radicals when simplifying algebraic expressions?

**Tip:** Always remember that the denominator in a fractional exponent represents the root, and the numerator represents the power!

Express the radical form \(\sqrt[3]{4^5}\) as an exponent.

Learn how to convert the radical expression \(\sqrt[3]{4^5}\) into its equivalent exponent form using the formula for fractional exponents. Suitable for Grades 9-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation