https://file.aiquickdraw.com/mathbot/file/172695580420969ohzogt.jpg

The expression in the image appears to be the sixth root of \( 11^3 \), written as:

\[
\sqrt[6]{11^3}
\]

This can be simplified or rewritten in exponential form. In terms of exponents, this is equivalent to:

\[
(11^3)^{\frac{1}{6}} = 11^{\frac{3}{6}} = 11^{\frac{1}{2}}
\]

Thus, the simplified result is:

\[
11^{\frac{1}{2}} = \sqrt{11}
\]

This represents the square root of 11. 

Would you like further clarification on this process or any additional details?

Here are five related questions to explore:
1. What are the steps to simplify higher-order roots of powers?
2. How can this expression be evaluated as a decimal approximation?
3. What are the properties of exponents when simplifying roots?
4. How would you handle an expression like \( \sqrt[6]{11^5} \)?
5. What is the difference between simplifying roots and evaluating them?

**Tip:** When simplifying radicals, remember that \( \sqrt[n]{a^m} = a^{\frac{m}{n}} \) helps convert roots into fractional exponents for easier manipulation!

What is the simplified form of the expression \( \sqrt[6]{11^3} \)?

Learn how to simplify the sixth root of \( 11^3 \), which can be rewritten in exponential form as \( 11^{1/2} \), equivalent to the square root of 11. This explanation covers radical simplification using properties of exponents. Suitable for students in Grades 9-11.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation