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

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1 answer

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

Applying this property to the left side of the equation:

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

Now, we can rewrite the equation:

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

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 \( \boxed{17} \).