Simplify 5^-3 × 5^-4: Negative Exponent Multiplication

To solve the problem of simplifying the expression $5^{-3} \times 5^{-4}$, we will apply the exponent multiplication rule, which states that when multiplying powers with the same base, we simply add their exponents.

• Step 1: Identify the expression and confirm both terms share the base of 5. They are $5^{-3}$ and $5^{-4}$.
• Step 2: Apply the exponent multiplication rule: $5^{-3} \times 5^{-4} = 5^{(-3) + (-4)}$.
• Step 3: Simplify the expression by adding the exponents: $-3 + (-4) = -7$.

Therefore, the expression simplifies to $5^{-7}$.

Given the possible choices, the correct answer is $5^{-7}$, which corresponds to choice (1).

Thus, the solution to the problem is $5^{-7}$.