Let's break down the expression \(\frac{8^{-1} \times 5^3}{2^4}\).

1. **Evaluate \(8^{-1}\)**:  
   \(8^{-1} = \frac{1}{8}\), since raising to the power of \(-1\) means taking the reciprocal.

2. **Evaluate \(5^3\)**:  
   \(5^3 = 5 \times 5 \times 5 = 125\).

3. **Evaluate \(2^4\)**:  
   \(2^4 = 2 \times 2 \times 2 \times 2 = 16\).

Now, substitute these values back into the expression:

\[
\frac{\frac{1}{8} \times 125}{16} = \frac{125}{8 \times 16} = \frac{125}{128}
\]

So, the final result is:

\[
\frac{125}{128}
\]

Would you like a detailed explanation of any step?

Here are 5 related questions:
1. What is \(8^{-2} \times 5^2\)?
2. How do you simplify \(\frac{4^{-1} \times 7^2}{3^3}\)?
3. What is the result of \(\left( \frac{6^2}{3^2} \right)^2\)?
4. How do you evaluate \(2^{-3} \times 3^4\)?
5. Can you simplify \(\frac{9^2}{3^4}\)?

**Tip**: Negative exponents flip the base, turning \(a^{-n}\) into \(\frac{1}{a^n}\).

Learn how to simplify the expression (8^-1 * 5^3) / 2^4 using exponent rules and fraction simplification techniques. This problem covers key mathematical concepts such as negative exponents and order of operations, making it ideal for students in Grades 6-8.

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