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 use the properties of exponents. According to the rules of exponents, when dividing two expressions with the same base, you subtract their exponents:

\[ \frac{7^m}{7^n} = 7^{m-n} \]

Applying this to our equation gives us:

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

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

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

Since the bases are the same, we can equate the exponents:

\[ ? - 5 = 12 \]

To find the value of \( ? \), we add 5 to both sides:

\[ ? = 12 + 5 = 17 \]

Thus, the missing number is:

\[ \boxed{17} \]