(-7 squared x squared y over y cubed) to the power of -1

To solve the expression \(\left(\frac{-7^2 x^2 y}{y^3}\right)^{-1}\), let's break it down step by step.

### Step 1: Simplify the expression inside the parentheses
The expression inside the parentheses is:
\[
\frac{-7^2 x^2 y}{y^3}
\]
First, calculate \(-7^2\):
\[
-7^2 = 49
\]
So the expression becomes:
\[
\frac{49 x^2 y}{y^3}
\]
Now simplify the \(y\)-terms. The \(y^1\) in the numerator cancels out one of the \(y\)'s in the denominator, leaving:
\[
\frac{49 x^2}{y^2}
\]

### Step 2: Apply the exponent of \(-1\)
Now, raise the expression \(\frac{49 x^2}{y^2}\) to the power of \(-1\). When an expression is raised to the power of \(-1\), the numerator and denominator are swapped:
\[
\left(\frac{49 x^2}{y^2}\right)^{-1} = \frac{y^2}{49 x^2}
\]

### Final Answer:
The simplified expression is:
\[
\frac{y^2}{49 x^2}
\]

Let me know if you'd like more details or have questions. Here are some related questions:

1. How do negative exponents affect fractions?
2. What is the rule for canceling variables in fractions?
3. How does exponentiation distribute over multiplication?
4. What is the significance of raising something to the power of zero?
5. How can you simplify more complex algebraic fractions?

**Tip:** When raising a fraction to a negative exponent, always remember that you are flipping the fraction!

This problem focuses on simplifying the expression (-7^2 x^2 y / y^3) to the power of -1 using exponent rules and algebraic fraction simplification. Step-by-step solution provided for Grades 8-10 students.

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