The given expression is:

\[
\frac{(9^{-8})^0}{9^{-4}}
\]

### Step-by-step solution:

1. **Simplify \((9^{-8})^0\)**: 
   Any non-zero number raised to the power of 0 equals 1. So:
   \[
   (9^{-8})^0 = 1
   \]

   Now the expression becomes:
   \[
   \frac{1}{9^{-4}}
   \]

2. **Simplify the denominator \(9^{-4}\)**:
   Using the negative exponent rule, \(a^{-n} = \frac{1}{a^n}\), we can rewrite \(9^{-4}\) as:
   \[
   9^{-4} = \frac{1}{9^4}
   \]

   So the expression now is:
   \[
   \frac{1}{\frac{1}{9^4}} = 9^4
   \]

### Final answer:

\[
9^4 = 6561
\]

So, the value of the given expression is **6561**.

Would you like more details or have any further questions?

Here are some related questions for further practice:

1. Simplify \(\frac{(5^{-3})^0}{5^{-2}}\).
2. Simplify \(\frac{(7^{-5})^2}{7^{-3}}\).
3. What is \(\frac{(2^3)^0}{2^{-2}}\)?
4. Evaluate \(\frac{(10^{-2})^0}{10^{-1}}\).
5. Simplify \(\frac{(3^{-6})^0}{3^{-5}}\).

**Tip:** Any base (except 0) raised to the power of 0 always equals 1!

Learn how to simplify the expression (9^ -8)^0/9^ -4 step-by-step. This problem covers exponentiation rules, negative exponents, and simplification techniques. The solution demonstrates the key concepts of exponent laws, making it ideal for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation