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Let's solve the expression step by step. The given expression is:

\[
\frac{4f^0 g^0}{2f^{-5}g^{-1}}
\]

### Step 1: Simplify using the properties of exponents.

- **Any number to the power of 0 equals 1**:
  \[
  f^0 = 1 \quad \text{and} \quad g^0 = 1
  \]
  So, the expression simplifies to:
  \[
  \frac{4 \times 1 \times 1}{2f^{-5}g^{-1}} = \frac{4}{2f^{-5}g^{-1}}
  \]

### Step 2: Simplify the constants.
\[
\frac{4}{2} = 2
\]
Now the expression is:
\[
\frac{2}{f^{-5}g^{-1}}
\]

### Step 3: Apply the exponent rule for negative exponents.
- \( f^{-5} = \frac{1}{f^5} \)
- \( g^{-1} = \frac{1}{g} \)

Thus, dividing by \( f^{-5}g^{-1} \) is the same as multiplying by \( f^5g^1 \):
\[
2 \times f^5 \times g = 2f^5g
\]

### Final Answer:
\[
2f^5g
\]

Would you like any additional clarification or details?

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Here are 5 related questions to consider:
1. What is the rule for multiplying powers with the same base?
2. How do negative exponents affect fractions?
3. Can you simplify an expression like \( a^{-3} \times b^{-2} \)?
4. How do you apply exponent rules when bases are different?
5. How does simplifying exponents change with division?

**Tip**: Always start by simplifying powers of 0, as they will cancel out early in the process!

Simplify. Express your answer using positive exponents. (4f^0g^0)/(2f^-5g^-1)

Learn how to simplify an expression with exponents like (4f^0g^0)/(2f^-5g^-1). This problem involves exponent rules, such as a^0 = 1 and a^-n = 1/a^n. Suitable for students in Grades 8-10.

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