Simplify the Expression: a^(-3) × a^5 × a^(-4)

The given expression is $a^{-3} \times a^5 \times a^{-4}$.

To simplify, use the product of powers property, which states that when multiplying like bases, you add the exponents:

• Apply the rule: $a^{-3} \times a^5 \times a^{-4} = a^{-3+5-4}$.
• Calculate the sum of the exponents: $-3 + 5 - 4 = -2$.

This simplifies the expression to $a^{-2}$.

Note that $a^{-2}$ can also be expressed as $\frac{1}{a^2}$ using the property of negative exponents $(a^{-n} = \frac{1}{a^n})$.

Now, let's evaluate the choices:

• Choice 1: $a^{-2}$, which matches our simplification.
• Choice 2: $\frac{1}{a^2}$, which is another form of $a^{-2}$.
• Choice 3: $a^{-3+5-4}$, which correctly reflects the intermediate step we computed.
• Choice 4 states "All answers are correct," which, considering all interpretations and simplifications are valid, is indeed true.

Therefore, the correct answer is: All answers are correct, as each choice corresponds to a logical step or equivalent expression in reducing the equation.