Question

what is the missing exponet n^365/ n^? =n^152

Answer 1

To solve for the missing exponent in the equation \( \frac{n^{365}}{n^?} = n^{152} \), we can use the properties of exponents.

According to the properties of exponents:

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

Applying this to our equation, we have:

\[
\frac{n^{365}}{n^?} = n^{365 - ?}
\]

Setting this equal to \( n^{152} \):

\[
n^{365 - ?} = n^{152}
\]

Since the bases are the same, we can set the exponents equal to each other:

\[
365 - ? = 152
\]

Now, we can solve for \( ? \):

\[
365 - 152 = ?
\]

Calculating the left side:

\[
? = 365 - 152 = 213
\]

Thus, the missing exponent is:

\[
? = 213
\]