0,5 hoch minus 2: Understanding Exponents with Negative Numbers
In mathematics, exponents play a crucial role in simplifying complex expressions and equations. One of the most common exponentiation operations is raising a number to a power, denoted by the caret symbol (^). However, things can get a bit tricky when dealing with negative numbers and fractional exponents. In this article, we'll explore the concept of 0,5 hoch minus 2 and learn how to evaluate such expressions.
What does 0,5 hoch minus 2 mean?
In German, "hoch" means "to the power of", so "0,5 hoch minus 2" translates to "0.5 to the power of minus 2". This expression can be written in mathematical notation as:
(0.5)^(-2)
How to evaluate 0,5 hoch minus 2
To evaluate this expression, we need to understand the rules of exponentiation. When dealing with fractional exponents, we can rewrite the expression using the rule:
a^(m/n) = (n√a)^m
where a is the base, m is the exponent, and n is the denominator of the fractional exponent.
In our case, we have:
(0.5)^(-2) = (2√0.5)^(-2)
Simplifying the radical, we get:
(2√0.5)^(-2) = (√2)^(-2)
Now, we can apply the rule of exponents that states:
a^(-n) = 1/a^n
So, we have:
(√2)^(-2) = 1/(√2)^2
Simplifying further, we get:
1/(√2)^2 = 1/2
Therefore, 0,5 hoch minus 2 equals 1/2.
Conclusion
In conclusion, evaluating expressions with fractional exponents and negative numbers requires a solid understanding of exponentiation rules. By applying these rules, we can simplify complex expressions and arrive at a solution. In this case, we found that 0,5 hoch minus 2 equals 1/2. This knowledge will help you navigate more complex mathematical problems with ease.
