What is the missing exponent in the following equation? s^500s^?=s^175 Note: only type the exponent in the box, do not include any variables. Show your work.

Answer 1

To solve for the missing exponent in the equation \( s^{500}s^{?}=s^{175} \), we can use the property of exponents that states \( a^m \cdot a^n = a^{m+n} \).

1. Apply the property of exponents: \[ s^{500} s^{?} = s^{500 + ?} \]

2. Set the equation equal to \( s^{175} \): \[ s^{500 + ?} = s^{175} \]

3. Since the bases are the same, we can set the exponents equal to each other: \[ 500 + ? = 175 \]

4. To find the value of \( ? \), we subtract 500 from both sides: \[ ? = 175 - 500 \]

5. Calculate: \[ ? = -325 \]

Thus, the missing exponent is \(-325\).