Question

What is the missing exponent in the following equation?

s500/s^?=s^175


Note: only type the exponent in the box, do not include any variables.

Show your work.

(1 point)

Answer 1

To find the missing exponent in the equation

\[
\frac{s^{500}}{s^{?}} = s^{175},
\]

we can use the property of exponents, which states that when you divide two expressions with the same base, you subtract the exponents. Therefore, we can express the left side of the equation as follows:

\[
s^{500 - ?} = s^{175}.
\]

Since both sides of the equation have the same base \(s\), we can set the exponents equal to each other:

\[
500 - ? = 175.
\]

Now, we can solve for the missing exponent \(?\):

1. Subtract 175 from both sides:

\[
500 - 175 = ?.
\]

2. Calculate the left side:

\[
325 = ?.
\]

Thus, the missing exponent is

\[
\boxed{325}.
\]