To solve this problem, we need to simplify the given expression with exponents:

$\frac{x^{-6} x^7 y^4}{y^5}$

Step 1: Simplify the $x$ terms

The terms involving $x$ in the numerator are $x^{-6}$ and $x^7$. Using the rule $x^a \cdot x^b = x^{a+b}$, we combine these exponents:

$x^{-6} \cdot x^7 = x^{-6 + 7} = x^1 = x$

Step 2: Simplify the $y$ terms

The $y$ terms in the expression are $y^4$ in the numerator and $y^5$ in the denominator. Using the division rule $\frac{y^a}{y^b} = y^{a-b}$, we get:

$\frac{y^4}{y^5} = y^{4 - 5} = y^{-1} = \frac{1}{y}$

Step 3: Combine the simplified terms

After simplifying both the $x$ and $y$ terms, we are left with:

$\frac{x}{y}$

Final Answer

The correct answer is: $\frac{x}{y}$

So, the answer choice to select is:

• $\frac{x}{y}$

Would you like further explanation on any steps or have questions about exponent rules?

Here are five related questions to deepen your understanding:

1. How would you simplify an expression like $\frac{x^3 y^{-2}}{x^{-1} y^4}$?
2. What is the result of $x^{-3} y^2 \cdot x^2 y^{-4}$?
3. How do you simplify expressions where both the numerator and denominator have multiple terms with negative exponents?
4. Can you explain why $x^0 = 1$ and how it affects simplifications?
5. What steps would you take to rewrite $\frac{x^{-2}}{y^{-3}}$ with only positive exponents?

Tip: Remember that negative exponents indicate a reciprocal. For example, $x^{-a} = \frac{1}{x^a}$. This can help in simplifying expressions by moving terms from the numerator to the denominator and vice versa.