Master Negative Exponents: Unlocking the Secrets of Reciprocals

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

• A. (5/7)^1
• B. (7/5)^1
• C. (7/5)^-1
• D. (5/7)^-1

Answer: (A)

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

When it comes to tackling basic math concepts, one topic that often trips students up is negative exponents. If you’re preparing for the Assessment and Learning in Knowledge Spaces (ALEKS) Basic Math Placement Test, understanding this concept is crucial. So, let's get into it, shall we?