Write the expression in exponential form.
cube root of, x, squared, end cube root
3
  
x 
2
 
​	
 

The expression "cube root of \( x^2 \)" can be written in exponential form using fractional exponents. 

The cube root of a number is the same as raising that number to the power of \( \frac{1}{3} \). So, the cube root of \( x^2 \) becomes:

\[
(x^2)^{\frac{1}{3}}
\]

Now, simplify the exponents:

\[
x^{2 \cdot \frac{1}{3}} = x^{\frac{2}{3}}
\]

Thus, the expression in exponential form is:

\[
x^{\frac{2}{3}}
\]

Would you like more details on how exponents work with roots, or do you have any other questions?

Here are five related questions for further practice:

1. How would you express the square root of \(x^3\) in exponential form?
2. What is the exponential form of the fourth root of \(x^5\)?
3. How do you simplify \((x^3)^{1/4}\)?
4. Can you express \( \frac{1}{\sqrt{x}} \) using exponents?
5. What is the cube root of \( x^6 \) in exponential form?

**Tip:** When dealing with roots, remember that the \( n \)-th root of a number can always be written as that number raised to the power of \( \frac{1}{n} \).

Write the expression in exponential form. Cube root of x squared.

Learn how to convert the cube root of x squared to exponential form. This solution explores fractional exponents and the laws of exponents, breaking down the cube root of x^2 step-by-step. Suitable for students in Grades 8-10.

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