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

1 answer

To solve the equation \( 7^? ÷ 7^5 = 7^{12} \), we can use the property of exponents which states that when you divide two exponential expressions with the same base, you can subtract the exponents:

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

So we can rewrite the equation as:

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

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

\[ ? - 5 = 12 \]

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

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

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