%5E-2-math.jpeg "(3/5)^-2 Math")
Understanding (3/5)^-2
In mathematics, negative exponents indicate reciprocals. This means that (3/5)^-2 is the same as 1 divided by (3/5) raised to the power of 2.
Here's how to break it down:
1. Reciprocals:
- The reciprocal of a fraction is simply flipping the numerator and denominator. So the reciprocal of (3/5) is (5/3).
2. Exponents:
- An exponent indicates how many times a number is multiplied by itself. In this case, (3/5)^2 means (3/5) multiplied by itself twice: (3/5) * (3/5).
3. Combining the concepts:
- (3/5)^-2 = 1 / (3/5)^2
- (3/5)^2 = (3/5) * (3/5) = 9/25
- Therefore, (3/5)^-2 = 1 / (9/25)
4. Simplifying the fraction:
- Dividing by a fraction is the same as multiplying by its reciprocal.
- So, 1 / (9/25) = 1 * (25/9) = 25/9
Final Answer:
(3/5)^-2 is equal to 25/9.
Key Takeaways:
- Negative exponents represent reciprocals.
- Exponents indicate repeated multiplication.
- Understanding the relationship between reciprocals and exponents is crucial for solving problems involving negative exponents.