https://file.aiquickdraw.com/mathbot/file/1727453429973aah3khwo.jpg

The expression in the image is:

\[
\frac{10y}{10y^7}
\]

To simplify this expression, we can break it down:

1. The constants \( 10 \) in both the numerator and denominator cancel each other out.
2. For the variable \( y \), we apply the property of exponents which says:

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

So, applying this to our expression:

\[
\frac{y}{y^7} = y^{1-7} = y^{-6}
\]

Thus, the simplified expression is:

\[
y^{-6} = \frac{1}{y^6}
\]

The final answer is:

\[
\frac{1}{y^6}
\]

Would you like more details on exponent rules or any other clarifications?

Here are 5 related questions to consider:
1. How do you simplify an expression with both constants and variables?
2. What is the significance of a negative exponent in algebra?
3. How do you apply the properties of exponents in division?
4. How would the expression change if the exponents were different?
5. What are some real-world applications of simplifying algebraic expressions?

**Tip:** When simplifying expressions with the same base, always remember to subtract exponents when dividing!

Learn how to simplify the expression 10y / 10y^7 by applying exponent rules. This problem demonstrates the concept of dividing terms with the same base, resulting in y^-6 or 1/y^6. Suitable for students in Grades 7-9.

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