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

1 answer

To solve the equation \( \frac{7^?}{7^5} = 7^{12} \), we can use the properties of exponents. Specifically, we can use the quotient rule, which states that \( \frac{a^m}{a^n} = a^{m-n} \).

Applying this rule, we have:

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

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

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

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

\[ ? - 5 = 12 \]

To find \( ? \), we solve for \( ? \):

\[ ? = 12 + 5 = 17 \]

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