Which expression is equivalent to x superscript negative five-thirds – This exploration delves into the intriguing realm of exponents, delving into the concept of negative exponents and their profound implications. At the heart of our inquiry lies the enigmatic expression “x superscript negative five-thirds.” Join us as we embark on a journey to unravel its mysteries and uncover its mathematical equivalents.
Our discourse will traverse a landscape of equivalent expressions, comparing and contrasting their nuances. Through the lens of mathematical operations, we shall witness the transformative power of negative exponents. The practical applications of these expressions will also be illuminated, showcasing their versatility in addressing real-world conundrums.
1. Introduction
Exponents are mathematical operators that indicate the number of times a base number is multiplied by itself. Negative exponents indicate that the base number is in the denominator of a fraction.
The expression “x superscript negative five-thirds” means that 1 is divided by x multiplied by itself five times and then multiplied by itself again three times: 1 / (x 5– x 3).
2. Equivalent Expressions
Several expressions are equivalent to “x superscript negative five-thirds”:
| Expression | Equivalent to x-5/3 |
|---|---|
| 1 / x5/3 | Yes |
| x-3/5 | No |
1 / (x3
|
Yes |
3. Mathematical Operations
Expressions with negative exponents can be simplified using the following rules:
- Multiplying two expressions with the same base and negative exponents adds the exponents: a -m– a -n= a -(m+n)
- Dividing two expressions with the same base and negative exponents subtracts the exponents: a -m/ a -n= a -(m-n)
- Raising an expression with a negative exponent to a positive exponent negates the exponent: (a -m) n= a -mn
4. Applications
Expressions with negative exponents have practical applications in various fields, including:
- Physics:Describing inverse square laws, such as the relationship between gravitational force and distance
- Economics:Modeling economic growth and decay
- Biology:Analyzing population growth and decline
Query Resolution: Which Expression Is Equivalent To X Superscript Negative Five-thirds
What is the definition of “x superscript negative five-thirds”?
It represents the reciprocal of x raised to the power of five-thirds, which is 1/(x^(5/3)).
Can you provide an example of an equivalent expression for “x superscript negative five-thirds”?
One equivalent expression is x^(-5/3), which is obtained by rewriting the negative exponent as a fraction with a negative numerator.
How do you simplify an expression involving a negative exponent?
To simplify, rewrite the expression with a positive exponent in the denominator. For instance, x^(-5/3) becomes 1/(x^(5/3)).
