What is the missing number in this simplified exponential expression: 7 rasied to the power of ?÷7 rasied to the power of 5=7 rasied to the power of 12

1 answer

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

When you divide two exponentials with the same base, you subtract the exponents:

\[ 7^{?} \div 7^{5} = 7^{(?) - 5} \]

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:

\[ ? - 5 = 12 \]

Now, we can solve for \( ? \):

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

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