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It looks like the worksheet focuses on rational exponents and roots. Let's break down the key sections:

### 1. Introduction to Rational Exponents:
The text discusses how roots like \( \sqrt[3]{1000} \) can be represented as powers, such as \( 1000^{1/3} = 10 \). It introduces the idea that roots can be expressed as exponents, following the rule:
\[
\sqrt[n]{a} = a^{\frac{1}{n}}
\]
and extends this to fractional exponents, showing the relationship between roots and powers.

### 2. Calculating Roots:
You are asked to calculate:
   - \( \sqrt[3]{81} \)
   - \( \sqrt[3]{72} \)
   - \( \sqrt{5} \)
   - \( \sqrt[7]{5^2} \)

The general process here involves applying the rules of fractional exponents:
   - \( \sqrt[n]{a} = a^{1/n} \)
   - \( \sqrt[n]{a^m} = a^{m/n} \)

### 3. Writing Expressions as Powers:
This section likely asks you to rewrite roots in the form of powers with fractional exponents. For example:
   - \( \sqrt[3]{72} \) would be written as \( 72^{1/3} \).

### 4. Comparing Equivalent Expressions:
There are some multiple-choice questions where you're asked to compare equivalent expressions of powers and roots, e.g., \( \sqrt[5]{5^2} \), \( 5^{2/5} \), etc.

Would you like me to solve these specific problems for you? If so, let me know which parts you'd like explained in more detail! 

Here are five follow-up questions to extend the topic:
1. What is the difference between an integer exponent and a rational exponent?
2. How do you simplify expressions with negative fractional exponents?
3. What is the general formula to convert a root to an exponent?
4. How do you solve an equation where the variable is in the exponent?
5. Can you explain how to apply rational exponents when dealing with large numbers?

**Tip:** Always remember that \( \sqrt[n]{a^m} = a^{m/n} \) can simplify many root problems!

The worksheet contains tasks related to rational exponents and roots. The questions involve calculating roots, rewriting expressions using rational exponents, and comparing equivalent expressions.

Learn how to solve problems involving rational exponents and roots, including calculating cube roots, converting expressions into fractional exponents, and understanding equivalent expressions. This worksheet is suitable for students in Grades 8-10.

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