What is the missing number in this simplified exponential expression:

7^?÷7^5=7^12

1 answer

To solve the equation \( 7^? ÷ 7^5 = 7^{12} \), we can use the properties of exponents.

When dividing two exponential expressions with the same base, we subtract the exponents:

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

Setting this equal to \( 7^{12} \):

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

Since the bases (7 in this case) are the same, we can set the exponents equal to each other:

\[ ? - 5 = 12 \]

Now, solve for \( ? \):

\[ ? = 12 + 5 \] \[ ? = 17 \]

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