https://file.aiquickdraw.com/mathbot/file/1729451878851441bhrr2.jpg

Let's break down and simplify both expressions.

### 1. First Expression: \(\frac{\frac{4}{3}}{8}\)

- This is equivalent to multiplying by the reciprocal:
\[
\frac{4}{3} \div 8 = \frac{4}{3} \times \frac{1}{8} = \frac{4 \times 1}{3 \times 8} = \frac{4}{24} = \frac{1}{6}
\]

Thus, the simplified result for the first expression is \( \frac{1}{6} \).

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### 2. Second Expression: \(\left( \frac{1}{125} \right)^{\frac{2}{3}}\)

- The cube root of 125 is 5, so we first simplify \( \left( \frac{1}{125} \right)^{\frac{1}{3}} = \frac{1}{5} \).
- Now square the result: 
\[
\left( \frac{1}{125} \right)^{\frac{2}{3}} = \left( \frac{1}{5} \right)^2 = \frac{1}{25}
\]

Thus, the simplified result for the second expression is \( \frac{1}{25} \).

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### Final Answers:
1. \( \frac{1}{6} \)
2. \( \frac{1}{25} \)

Let me know if you'd like more details or have any questions!

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Here are 5 follow-up questions:
1. How do you multiply fractions?
2. What are the rules for dividing by a fraction?
3. How do you calculate the cube root of a number?
4. What are fractional exponents, and how do they work?
5. How can exponentiation with fractions be used to simplify radicals?

**Tip:** When simplifying complex expressions, try to break them down step by step, simplifying small parts first before recombining them.

Simplify the following expressions without exponents: 1) (4/3) ÷ 8 2) (1/125)^(2/3)

Learn how to simplify expressions like (4/3) ÷ 8 and (1/125)^(2/3) without using exponents. This tutorial covers key concepts such as fraction division, exponentiation, and radical simplification, making it suitable for students in Grades 8-10.

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