Question

What is the missing number in this simplified exponential expression:
7^? dived by 7^5 = 7^12
(1 point)

Answer 1

To solve for the missing number in the expression \( \frac{7^?}{7^5} = 7^{12} \), we can use the properties of exponents.

When dividing like bases, we subtract the exponents:

\[
\frac{7^a}{7^b} = 7^{a-b}
\]

Applying this to our expression:

\[
\frac{7^?}{7^5} = 7^{? - 5}
\]

Setting this equal to the right side of the equation, we have:

\[
7^{? - 5} = 7^{12}
\]

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

\[
? - 5 = 12
\]

Now, we solve for \( ? \):

\[
? = 12 + 5 = 17
\]

Thus, the missing number is \( \boxed{17} \).