https://file.aiquickdraw.com/mathbot/file/17260522283190ttv4pfk.jpg

The expression given in the image is \( 7^8 \div 7^{11} \).

To simplify this, we can apply the rule for division of exponents, which states:

\[
\frac{a^m}{a^n} = a^{m-n}
\]

Using this rule:

\[
7^8 \div 7^{11} = 7^{8 - 11} = 7^{-3}
\]

This can be further simplified to:

\[
7^{-3} = \frac{1}{7^3}
\]

Thus, the correct answer is **A: \( \frac{1}{7^3} \)**.

Would you like further details or have any other questions? Here are 5 related questions that might help expand your understanding:

1. How do you simplify expressions with different bases?
2. What are the rules for multiplying exponents?
3. Can you apply the exponent rule for fractional exponents?
4. How does a negative exponent change the expression?
5. What happens if the exponents are negative in both terms of the division?

**Tip:** Whenever you encounter division of exponents with the same base, subtract the exponent in the denominator from the exponent in the numerator.

Learn how to simplify the exponent expression 7^8 ÷ 7^11 using the laws of exponents. This step-by-step guide shows how to apply the exponent division rule and the negative exponent rule. Suitable for students in Grades 8-10.

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