Kaplan Nursing Entrance Practice Exam

What does 7 subscript 12 divided by 7 subscript 3 equal?

1. 7 subscript 9

2. 7 subscript 15

3. 7 subscript 12

4. 7 subscript 3

The correct answer is: 7 subscript 9

To solve the expression \( 7_{12} \div 7_{3} \), we can apply the laws of exponents. When dividing two exponential terms with the same base, we subtract the exponents. Here, we have: \[ 7_{12} \div 7_{3} = 7^{12 - 3} = 7^{9} \] Thus, the result simplifies to \( 7_{9} \). This demonstrates the property of exponents effectively, allowing us to conclude that the correct answer is indeed \( 7_{9} \). By understanding this exponent rule, it is clear that \( 7_{12} \) divided by \( 7_{3} \) results in a new expression with a base of 7 and an exponent that is the difference between the two original exponents.