Question

What is the missing exponent in the following equation?

s500s?=s175


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 \( s^{500} s^\text{?} = s^{175} \), we can use the properties of exponents. The property that applies here is \( s^a s^b = s^{a+b} \).

Using that property, we can rewrite the left side of the equation:

\[
s^{500} s^\text{?} = s^{500 + \text{?}}
\]

Now we can set the left side equal to the right side:

\[
s^{500 + \text{?}} = s^{175}
\]

Since the bases (s) are the same, we can equate the exponents:

\[
500 + \text{?} = 175
\]

To find the value of the missing exponent (?), we can rearrange the equation:

\[
\text{?} = 175 - 500
\]

Calculating that gives:

\[
\text{?} = -325
\]

Thus, the missing exponent is:

\[
\boxed{-325}
\]