What is the missing number in this simplified exponential expression:

7^? ÷ 7^5 = 7^12

1 answer

To solve the equation \( \frac{7^?}{7^5} = 7^{12} \), we can apply the property of exponents that states \( \frac{a^m}{a^n} = a^{m-n} \).

Using this property, we rewrite the left side of the equation:

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

Now, we have:

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

Since the bases (7) are the same, we can equate the exponents:

\[ ? - 5 = 12 \]

To solve for \( ? \), we add 5 to both sides:

\[ ? = 12 + 5 \]

\[ ? = 17 \]

Therefore, the missing number is

\[ \boxed{17} \]