https://file.aiquickdraw.com/mathbot/file/1727880485915ktxjwc44.jpg

Let's analyze and solve the expression given in the image, which is:

\[
\frac{6^{-6}}{6^{-8}} \times 6^4
\]

### Step 1: Simplify the fraction

Using the properties of exponents, specifically the rule \(\frac{a^m}{a^n} = a^{m-n}\), we can simplify the first part of the expression:

\[
\frac{6^{-6}}{6^{-8}} = 6^{-6 - (-8)} = 6^{-6 + 8} = 6^2
\]

### Step 2: Multiply the simplified fraction by \(6^4\)

Now the expression becomes:

\[
6^2 \times 6^4
\]

Using the rule for multiplying exponents with the same base \(a^m \times a^n = a^{m+n}\), we can simplify this further:

\[
6^2 \times 6^4 = 6^{2+4} = 6^6
\]

### Final Answer:

The expression is equivalent to:

\[
6^6
\]

Would you like any further clarification or details?

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Here are 5 related questions for further practice:
1. What is \( \frac{a^3}{a^2} \times a^5 \)?
2. Simplify the expression \( \frac{7^{-3}}{7^{-5}} \times 7^8 \).
3. How would you simplify \( \frac{5^6}{5^2} \times 5^3 \)?
4. If \( x = 2^4 \times 2^{-2} \), what is the value of \(x\)?
5. What is the result of \( 10^{-3} \times 10^5 \)?

**Tip:** When simplifying expressions involving exponents, always apply the exponent rules for division and multiplication to reduce complexity efficiently.

Which expression is equivalent to \( \frac{6^{-6}}{6^{-8}} \times 6^4 \)?

Learn how to simplify the expression \( \frac{6^{-6}}{6^{-8}} \times 6^4 \) using the laws of exponents. This step-by-step guide covers exponent division and multiplication rules, ideal for students in Grades 8-10.

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