Simplify the Expression: 7^(-2) × 7^(-3) × 7^5 Using Laws of Exponents

To solve for the expression $7^{-2}\times7^{-3}\times7^5$, we will apply the exponent rule where we add the exponents when multiplying powers with the same base.

Step 1: Identify the exponents in the expression:

• First term has exponent $-2$
• Second term has exponent $-3$
• Third term has exponent $5$

Step 2: Use the exponent rule $a^m \times a^n = a^{m+n}$

We add the exponents: $-2 + (-3) + 5$.

Step 3: Calculate the sum of the exponents:

$-2 + (-3) + 5 = -2 - 3 + 5 = -5 + 5 = 0$

Therefore, the simplified expression is $7^0$.

However, the task specifically asks us to represent the step incorporating the exponent change. In this step, it should reflect as:

$7^{-2-3+5}$, indicating the addition process before simplification to 0. Let's consider the provided choices:

The correct choice from the list provided that matches our transformation is:

• Choice 4: $7^{-2-3+5}$

Hence, the expression $7^{-2}\times7^{-3}\times7^5$ can be represented by the expression $7^{-2-3+5}$.

Therefore, the correct representation is $7^{-2-3+5}$.