To simplify the expression \(\frac{12y^{-4}}{y^3}\), we can use the laws of exponents. Here’s the step-by-step process:

1. **Rewrite the expression**: 
   \[
   \frac{12y^{-4}}{y^3}
   \]

2. **Apply the quotient rule for exponents**:**\(\frac{a^m}{a^n} = a^{m-n}\)**
   
   Here, the base \(y\) is the same, so subtract the exponents:
   \[
   y^{-4 - 3} = y^{-7}
   \]

3. **Simplify the expression**:
   \[
   12y^{-7}
   \]

4. **Convert the negative exponent to a positive one**: 

   Using the rule \(a^{-m} = \frac{1}{a^m}\), we can rewrite \(y^{-7}\) as \(\frac{1}{y^7}\).

5. **Final simplified form**:
   \[
   12y^{-7} = \frac{12}{y^7}
   \]

So, the simplified form of \(\frac{12y^{-4}}{y^3}\) is \(\frac{12}{y^7}\).

Would you like more details or have any questions?

Here are some related questions to expand on this topic:

1. How would you simplify the expression \(\frac{8x^{-5}}{x^2}\)?
2. What is the simplified form of \(\frac{5a^{-3}}{a^{-2}}\)?
3. How do you simplify \(\frac{15b^0}{b^4}\)?
4. Can you explain why \(y^{-7}\) is equal to \(\frac{1}{y^7}\)?
5. How does the power of a product rule work in exponentiation?

**Tip**: Remember that a negative exponent indicates a reciprocal. For example, \(y^{-n} = \frac{1}{y^n}\).

Simplify the algebraic expression 12y⁻⁴/y³ using the laws of exponents. This problem covers the quotient rule for exponents and the negative exponent rule, making it ideal for students in Grades 8-10.

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