https://file.aiquickdraw.com/mathbot/file/1725920833597nm3ckfki.jpg

The expression given is:

\[
c = \left( \sqrt[3]{68.1} \right)^3
\]

To simplify this, note that raising the cube root of a number to the power of 3 cancels out the cube root. So we have:

\[
c = 68.1
\]

Thus, the solution for \(c\) is:

\[
c = 68.1
\]

Would you like further explanation on cube roots, or any additional details on simplifying expressions like this?

Here are five related questions to explore:
1. What is the general rule for simplifying \( (\sqrt[n]{x})^n \)?
2. How would you solve for \( c \) if the expression had an additional term or exponent, such as \( \left( \sqrt[3]{68.1} + 2 \right)^3 \)?
3. Can the number 68.1 be expressed in terms of prime factors, and how would this affect the simplification?
4. How do you simplify radical expressions with fractions, such as \( \left( \sqrt[3]{68.1} \right)^{5/3} \)?
5. What are the steps to manually calculate cube roots without a calculator?

**Tip:** When simplifying expressions involving roots and powers, remember that the root and the power can often cancel each other out when the indices match (e.g., cube root and cube).

Solve for c. Express your answer in simplest radical form if necessary. c = (∛(68.1))^3

Learn how to solve and simplify the expression c = (∛68.1)^3 by canceling out the cube root with a step-by-step explanation. This solution applies the basic principles of radicals and exponents, making it perfect for students in Grades 9-10.

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