Simplify the following expression, writing your answer with only positive exponents.

y−2y−7

To simplify the expression \(\frac{y^{-2}}{y^{-7}}\), you can apply the rule of exponents:

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

In this case, \(a = y\), \(m = -2\), and \(n = -7\). Using the exponent rule:

\[
y^{-2 - (-7)} = y^{-2 + 7} = y^5
\]

Thus, the simplified expression is:

\[
y^5
\]

### Do you want more details or have any questions?

Here are 5 related questions to deepen your understanding:
1. What happens if both exponents are positive in a similar division problem?
2. How would you simplify \(\frac{y^4}{y^{-3}}\)?
3. What is the rule for multiplying powers of the same base?
4. How would you simplify an expression like \(\frac{x^{-5}}{x^{-2}}\)?
5. Can you explain why dividing powers leads to subtracting exponents?

**Tip:** When working with exponents, always remember to simplify negative exponents by converting them to their positive equivalent (e.g., \(x^{-n} = \frac{1}{x^n}\)).

Simplify the following expression, writing your answer with only positive exponents: y−2/y−7

Learn how to simplify expressions with negative exponents, such as y^-2 / y^-7, using the laws of exponents. This solution explains key algebraic concepts and provides a step-by-step guide to converting negative exponents into positive ones. Perfect for students in Grades 8-10.

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