What is the missing number in this simplified exponential expression:

7^? dived by 7^5 = 7^12
(1 point)

1 answer

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 \( \boxed{17} \).