https://file.aiquickdraw.com/mathbot/file/1729809772025nt5y7joq.jpg

Let's solve each expression step-by-step.

### First expression: 
\[
\frac{-4}{3} \div 8
\]

Dividing by a number is the same as multiplying by its reciprocal. So, we rewrite the division as multiplication:
\[
\frac{-4}{3} \times \frac{1}{8} = \frac{-4 \times 1}{3 \times 8} = \frac{-4}{24}
\]
Now simplify the fraction:
\[
\frac{-4}{24} = \frac{-1}{6}
\]

### Second expression: 
\[
\left( \frac{1}{125} \right)^{\frac{2}{3}}
\]

This is a fractional exponent. To simplify it:
- The denominator of the exponent, 3, indicates the cube root.
- The numerator, 2, means we square the result.

First, find the cube root of \(\frac{1}{125}\):
\[
\sqrt[3]{\frac{1}{125}} = \frac{1}{5}
\]

Now, square it:
\[
\left(\frac{1}{5}\right)^2 = \frac{1}{25}
\]

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

Would you like more details on any of these steps?

Here are 5 related questions to practice:
1. Simplify: \(\frac{-5}{4} \div 10\)
2. Simplify: \(\left( \frac{1}{64} \right)^{\frac{2}{3}}\)
3. Simplify: \(\frac{-6}{5} \times \frac{2}{3}\)
4. Simplify: \(\left( \frac{1}{27} \right)^{\frac{2}{3}}\)
5. Simplify: \(\frac{-7}{2} \div 14\)

**Tip**: When dividing fractions, always multiply by the reciprocal of the second fraction.

Simplify the expressions: -4/3 ÷ 8 and (1/125)^(2/3). Write your answers without exponents.

Learn how to simplify the expressions -4/3 ÷ 8 and (1/125)^(2/3) with a detailed step-by-step solution. This problem involves fraction division and fractional exponents, suitable for students in Grades 8-10.

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