Simplify the Expression: a^-3 × y^7 × a^-4 × y^-5 Using Exponent Rules

To simplify the given expression $a^{-3} \times y^7 \times a^{-4} \times y^{-5}$, we will apply the exponent rules.

First, let's handle the terms involving the base $a$:

$a^{-3} \times a^{-4}$

According to the rule $x^m \times x^n = x^{m+n}$, we add the exponents:

$a^{-3} \times a^{-4} = a^{-3 + (-4)} = a^{-7}$

Next, consider the terms involving the base $y$:

$y^7 \times y^{-5}$

Using the same exponent rule:

$y^7 \times y^{-5} = y^{7 + (-5)} = y^2$

The entire expression now becomes:

$a^{-7} \times y^2$

Thus, the simplified form of the given expression is $a^{-7} \times y^2$.