Question
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Tutor-Verified Answer
Answer
Solution
-
Recall the rule for negative exponents:
-
Apply the rule to
:
Thus,
expressed as a fraction in simplest form is
.
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The Deep Dive
To express
as a fraction, we can rewrite it using the definition of negative exponents. The expression
is equivalent to
, which simplifies to
.
So,
as a fraction in simplest form is
.
Now let’s consider some context around this transformation! In mathematics, negative exponents essentially represent the reciprocal of positive exponents. This means that when you encounter something like
, it simply means
. This is a nifty trick that is applicable in many areas, including algebra and calculus!
As for real-world applications, the concept of negative exponents is particularly handy when dealing with measurements and conversions in science. For example, in physics, you might have equations involving force, where small quantities are often represented with negative exponents. Understanding how to manipulate them helps simplify complex equations and enables clearer communication of scientific ideas!