4f to the negative 8th power divided by 2f to the zero power

Let's break down the expression:

\[
\frac{4f^{-8}}{2f^0}
\]

### Step 1: Simplify \( f^0 \)
Any non-zero number or variable raised to the power of zero equals 1. Therefore, \( f^0 = 1 \), so we can simplify the expression:

\[
\frac{4f^{-8}}{2 \cdot 1} = \frac{4f^{-8}}{2}
\]

### Step 2: Divide the constants
Now, we divide 4 by 2:

\[
\frac{4}{2} = 2
\]

So the expression becomes:

\[
2f^{-8}
\]

### Step 3: Simplify the negative exponent
A negative exponent indicates a reciprocal, so \( f^{-8} = \frac{1}{f^8} \). Substitute this into the expression:

\[
2f^{-8} = \frac{2}{f^8}
\]

### Final Answer
\[
\frac{4f^{-8}}{2f^0} = \frac{2}{f^8}
\]

Would you like more details on any part of this solution?

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1. How does exponent zero affect terms in a mathematical expression?
2. What rules govern division of terms with exponents?
3. How are negative exponents simplified in fractions?
4. Can exponent rules be applied to variables with different bases?
5. What are the steps to evaluate an expression with multiple exponent rules?

**Tip:** Remember, \( x^0 = 1 \) for any non-zero \( x \), a key simplification in algebra!

This page provides a step-by-step solution to simplify the expression 4f^-8 / 2f^0. Learn how to handle negative exponents, apply exponent rules, and simplify expressions involving zero and negative powers. Suitable for students in Grades 8-10.

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