Assessment and Learning in Knowledge Spaces (ALEKS) Basic Math Placement Practice Test

What is the result of (7/5) raised to the power of -1?

1. (5/7)^1

2. (7/5)^1

3. (7/5)^-1

4. (5/7)^-1

The correct answer is: (5/7)^1

To determine the result of raising \( \frac{7}{5} \) to the power of -1, it's important to understand the concept of negative exponents. A negative exponent indicates the reciprocal of the base raised to the opposite (positive) exponent. When we have \( \left( \frac{7}{5} \right)^{-1} \), it translates to the reciprocal of \( \frac{7}{5} \), which is calculated as follows: \[ \left( \frac{7}{5} \right)^{-1} = \frac{1}{\frac{7}{5}} = \frac{5}{7} \] Thus, \( \left( \frac{7}{5} \right)^{-1} \) simplifies to \( \frac{5}{7} \), which can also be expressed as \( \left( \frac{5}{7} \right)^1 \). Choosing the correct option, we find that the answer corresponds to the form of the result, which is indeed \( \left( \frac{5}{7} \right)^1 \). This demonstrates that understanding negative exponents and their relationship to reciprocals is key in arriving