https://file.aiquickdraw.com/mathbot/file/17272729702579roqw70m.jpg

The expression shown in the image is:

\[
9^4 \cdot 9^{-5}
\]

### Step-by-Step Solution:

1. When multiplying powers with the same base, you can add the exponents. The rule is:

\[
a^m \cdot a^n = a^{m+n}
\]

2. Apply this to the expression:

\[
9^4 \cdot 9^{-5} = 9^{4 + (-5)} = 9^{-1}
\]

3. Simplify the exponent:

\[
9^{-1} = \frac{1}{9}
\]

### Final Answer:

\[
\boxed{\frac{1}{9}}
\]

Would you like more details or have further questions?

---

Here are some related questions for further practice:

1. Simplify: \( 3^7 \cdot 3^{-2} \)
2. Simplify: \( 8^3 \cdot 8^2 \)
3. Evaluate: \( 5^6 \cdot 5^{-8} \)
4. Simplify: \( 2^4 \cdot 2^{-4} \)
5. What is the value of \( 7^{-2} \)?

**Tip:** Remember, multiplying powers of the same base means adding the exponents!

Learn how to simplify the expression 9^4 · 9^-5 using the laws of exponents. This problem demonstrates how to add exponents with the same base and simplifies to 1/9. Suitable for Grade 8 students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation