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

7
?
÷
7
5
=
7
12
?(1 point)

1 answer

To solve for the missing exponent in the expression \( 7^? \div 7^5 = 7^{12} \), we can use the laws of exponents.

Using the rule of exponents that states \( a^m \div a^n = a^{m-n} \), we can rewrite the left side of the equation as:

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

Since the bases are the same (both are \( 7 \)), we can set the exponents equal to each other:

\[ ? - 5 = 12 \]

Now, solve for \( ? \):

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

Therefore, the missing number is \( 17 \).