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Negative exponents might seem tricky at first, but they follow a simple rule. A negative exponent means that the base should be moved to the denominator to become positive. For example, if you have the expression \(a^{-b}\), you can rewrite it as \(\frac{1}{a^b}\). This is exactly what happens in the given problem.

Consider the expression \(w^{-3/4}\). According to the rule of negative exponents, we can rewrite it as \(\frac{1}{w^{3/4}}\). This simplification helps us move on to further conversions, like transitioning into radical notation.

Radical notation is another way to express exponents, particularly fractional ones. The radical sign \(\sqrt{}\) refers to the root of a number. Converting from an exponent to radical notation helps in visualizing and sometimes simplifying expressions.

In the problem, we need to convert the expression \(\frac{1}{w^{3/4}}\) to radical notation. A fractional exponent like \(3/4\) can be split into a root (denominator) and a power (numerator). Here's how you can do it:

The denominator 4 becomes the root. So we write the base \(w\) under a fourth root sign: \(\sqrt[4]{}\).
The numerator 3 becomes the power inside the root: \(w^3\).
Therefore, \(w^{3/4}\) converts to \(\sqrt[4]{w^3}\).
Bringing everything together, we get \(\frac{1}{\sqrt[4]{w^3}}\).

Understanding fractional exponents can be a game-changer in simplifying expressions. A fractional exponent is a way to represent both the root and the power of a number. For example, \(a^{m/n}\) translates to \(\sqrt[n]{a^m}\), where:

• The numerator (m) represents the exponent of the base inside the root.
• The denominator (n) represents the root level.

Let's use the exercise's expression \(\frac{1}{w^{3/4}}\). Here:

• 3 is the numerator, meaning the exponent applied to the base \(w\).
• 4 is the denominator, meaning we take the fourth root of the base \(w\).

Converting this into radical notation gives us \(\frac{1}{\sqrt[4]{w^3}}\), making it easier to work with in various mathematical problems.