Question

what is the missing exponent in the following equation?
8^500/8^? = 8^175

Answer 1

To solve the equation \( \frac{8^{500}}{8^{?}} = 8^{175} \), we can use the property of exponents that states:

\[
\frac{a^m}{a^n} = a^{m-n}
\]

Applying this to our equation, we can rewrite the left side:

\[
8^{500 - ?} = 8^{175}
\]

Since the bases are the same (both are 8), we can set the exponents equal to each other:

\[
500 - ? = 175
\]

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

\[
500 - 175 = ?
\]

Calculating this gives:

\[
? = 325
\]

So, the missing exponent is \( 325 \).