%5E-2.jpeg "(9/5)^-2")
Understanding (9/5)^-2
In mathematics, exponents indicate how many times a base number is multiplied by itself. When dealing with negative exponents, we are essentially dealing with the reciprocal of the base raised to the positive equivalent of the exponent. Let's break down the calculation of (9/5)^-2.
Key Concepts:
- Negative Exponent: A negative exponent indicates the reciprocal of the base raised to the positive version of the exponent.
- Fractional Exponent: A fractional exponent represents a root. For example, x^(1/2) is the square root of x.
Solving (9/5)^-2:
- Reciprocal: (9/5)^-2 is equivalent to (5/9)^2.
- Squaring: (5/9)^2 means multiplying (5/9) by itself.
- Calculation: (5/9) * (5/9) = 25/81
Therefore, (9/5)^-2 is equal to 25/81.
Visualizing with a Calculator:
You can use a calculator to verify the result. Most calculators allow you to input fractions and negative exponents directly.
Applications:
Understanding negative exponents is crucial in various fields like:
- Science: For expressing quantities like volume, mass, and density.
- Finance: For calculating compound interest and loan repayments.
- Computer Science: For working with binary numbers and data storage.
Conclusion:
While seemingly complex, calculating expressions like (9/5)^-2 simply involves applying the rules of exponents and reciprocals. By understanding these concepts, we can confidently solve such expressions and apply them in various fields.